There are growing calls for Joe Biden to use his new executive order sanctioning violent Israeli settlers to also target political leaders, including government ministers, responsible for driving attacks against Palestinians.

Pro-Israel groups and others in the US say the order is potentially a severe blow to the settlement movement in the West Bank, in part because financial sanctions could block even Israeli banks from doing business in parts of the occupied territories.

Human rights groups also want to see the measures used to stop US groups from donating tens of millions of dollars each year to the settlers.

The Biden administration has not said how widely it will apply the order after initially imposing sanctions against just four settlers responsible for escalating attacks on Palestinians, including forcing entire villages from their homes.

Josh Paul, a former state department official who resigned over the US supplying weapons for Israel’s present war in Gaza, said that the order is framed broadly enough for the administration to pursue those enabling and facilitating a surge in killings, beatings and forced removals. It is driven in part by far-right members of the government, such as the national security minister Itamar Ben-Gvir, intent on removing Palestinians as a step toward annexation of all or parts of the occupied territories.

“I think the order could and should implicate members of the current Israeli government, including Ben-Gvir but not only,” said Paul.

“The order is a small step forward and incremental one. On the one hand, I would say it certainly doesn’t go far enough. But also it does have the potential to be used a lot more than it has been so far.”

Michael Schaeffer Omer-Man, research director for Israel-Palestine at the group founded by the assassinated Saudi writer Jamal Khashoggi, Democracy for the Arab World Now, said that if the sanctions were expansively applied they could have a significant impact.

“The potential is to completely defund the settlement movement and the organisations that support it. It’s a very broad, powerful, weapon. But we have to see how they use it,” he said.

Paul suspects the order is a warning shot to pressure the Israeli government to rein in the settlers, who often act under the protection of the Israeli military or police, out of concern that the violence could explode into full scale conflict in the West Bank. But he questions whether Biden is interested in addressing the wider issue of the settlements, and the 700,000 Israelis living in the occupied territories, as an obstacle to peace.

“The problem isn’t violent settlers. They’re low-hanging fruit. The problem is the settlement enterprise and that is an enterprise that is funded, supported, enabled through US private donations and through US government tacit support. Occasionally secretaries of state or presidents pop up to condemn new settlement announcements but then do absolutely nothing to get in the way of that construction happening,” he said.

Others see the order as a chance to change the face of the settlement movement.

T’ruah, a New York-based group of rabbis campaigning for human rights, welcomed Biden’s order as “a really positive first step that has a lot of potential”. But T’ruah’s director, Rabbi Jill Jacobs, said the White House should follow up by targeting “the real leaders of the violent settler movement, including the heads of organisations that are inciting this violence”.

“There are a number of settler organisations in Israel whose leadership has been indicted, even in some cases convicted, in Israel of incitement and terror. The next step is to look at the leaders of those organisations,” she said.

Jacobs said that included much more prominent figures than the four obscure settlers already sanctioned, including present and former members of the Israeli parliament. She said Biden’s order should also be used to stop American organisations funding extremist Jewish groups in the occupied territories, including some with with close ties to the Kach movement, founded by the extremist American-born rabbi Meir Kahane and banned in Israel as a terrorist group.

“They’re also funding yeshivas like Od Yosef Chai in Yitzhar, one of the most extreme settlements. There are often settler attacks that originate from that settlement incited by the rabbis at the yeshiva,” she said.

In a rare prosecution of a rabbi, Yosef Elitzur of Yitzhar was convicted three years ago of inciting violence against Palestinians. Another of the yeshiva’s rabbis wrote a book claiming religious law permits Jews to kill gentile babies because of “the future danger that will arise if they are allowed to grow into evil people like their parents”.

In 2015, the Israeli newspaper Haaretz revealed that at least 50 organisations across the US were involved in fundraising for Israeli settlements.

T’ruah has previously asked the US tax authorities to investigate several American groups it accuses of funding Lehava, the Yitzhar yeshiva and other settlements with a history of violence or extremist groups. These include the New York-based Central Fund of Israel which also helps finance the Israel Land Fund which responsible for the expulsion of Palestinian families from their homes to make way for Jewish settlers.

Jacobs said money raised in the US also goes to Honenu, a group associated with Ben-Gvir, that gives cash payments to Israelis convicted of terrorism, including Yigal Amir, who assassinated the prime minister Yitzhak Rabin in 1995.

Another US group, Friends of Ir David, funds Elad, an Israeli settler organisation responsible for the forced removal of Palestinians as it seeks to “Judaise” occupied East Jerusalem.

Biden’s order bars individuals from travelling to the US and freezes their assets there. It quickly became evident that the measures could have a significant effect on settlers who have no direct connection with the US after Israeli banks froze accounts belonging to the targeted individuals so as to comply with American law.

Omer-Man said imposing sanctions on a wide range of settler leaders and those who support them could have a real impact.

“Take somebody living in a settlement. They have a mortgage. If they’re on the sanctions list, what happens to the mortgage? Does the Israeli bank cancel it? Does the Israeli government create a bank just to give mortgages to settlers which is then itself open to sanctions. The Jewish National Fund and the World Zionist Organization are involved designating and giving land to settlers which is inherently a part of the system,” he said.

“But none of that happens without political will. We don’t know what the red lines are, the triggers that the administration has set internally for when they’re going to expand the sanctions. If they don’t at least come up with a second round, then they won’t have created deterrence. It seems ridiculous to sanction these four individuals who are nobodies but it’s not really targeting them. It’s targeting the Israeli government.”

Paul said the Biden administration is genuinely concerned at events in the West Bank.

“I think the Biden administration understands the immense and imminent risk of a collapse of the Palestinian Authority in the West Bank, which would be an absolute catastrophe,” he said.

But Paul added that the sanctions order was also a domestic political move, arriving in the face of strong criticism from Arab American voters and many more liberal Democrats over Biden’s support for Israel attack on Gaza even as the Palestinian death toll rose into the tens of thousands.

“I had a conversation a couple of days ago with an Arab American activist who told me that the settler sanctions were announced they got 50 texts from the administration saying, ‘Look at what we’re doing, isn’t this great?’ So it goes to show that there is inherently a political aspect to this,” said Paul.