Mr Blinken’s remarks echoed the broader pushback in Washington over the court’s decision.
At least two measures imposing sanctions on the ICC had already been introduced in Congress as the court ramped up its inquiry into Israel’s handling of the war in Gaza.
Support on Capitol Hill appears to be coalescing around a bill launched earlier this month by Texas Republican Chip Roy.
The Illegitimate Court Counteraction Act would target ICC officials involved with the case by blocking their entry to the US, revoking any current US visas they hold, and prohibiting them from any property transactions within the country – unless the court ceases its cases against “protected persons of the United States and its allies”.
At least 37 lawmakers in the Republican-led House are now co-sponsoring the legislation, including Elise Stefanik, the chamber’s third-highest-ranking Republican.
Ms Stefanik is fresh off a visit to Israel, where she met with Mr Netanyahu, spoke at the Knesset, and met with the families of hostages trapped in Gaza.
The court “equivocates a peaceful nation protecting its right to exist with radical terror groups that commit genocide”, she told the BBC in a statement.
Andy Barr of Kentucky, another Republican supporting the bill, said the further pursuit of the ICC’s case against Israel must “be met with the full force of our sanctions”.
Less clear, however, is whether Democratic lawmakers will get behind the effort.
The party’s moderate and liberal wings have grappled with Mr Biden’s Israel policy for months, as young progressive voters have pushed the president to criticize the Netanyahu government’s operations in Gaza.
Ohio’s Greg Landsman, one of a few Democrats who voted last week to reverse Mr. Biden’s pause on a weapons shipment to Israel, told the BBC he hopes Congress will issue a bipartisan rebuke of the ICC “to send the strongest message possible”.
“The decision [to seek arrest warrants] will only further inflame tensions and divisions, embolden anti-Israel conspiracies, and ultimately, it will undermine the credibility of the ICC,” he said in a statement.
Republican House Speaker Mike Johnson urged Chuck Schumer, the Senate’s top Democrat, to sign a letter on Tuesday inviting Mr Netanyahu to address a joint meeting of Congress.
In March, Mr Schumer called for new elections in Israel but he described the ICC’s case on Monday as “reprehensible”.
Sen Chris Coons, a Democrat from Delaware and member of the Senate Foreign Relations Committee told the BBC that he was unsure about moves to sanction ICC officials.
“I’m not there yet imposing sanctions on the ICC, as opposed to looking to see whether the off ramp of a ruling by the judges of the ICC that they’re not going to proceed with warrants is something I think may come in the next couple of days,” the Democrat said.
But Mr Coons added that he is discussing taking action with his committee colleagues from both parties.
However, some left-wing Democrats have expressed their support for the ICC’s actions.
Minnesota Congresswoman Ilhan Omar said the court’s allegations are “significant” and the US must support its work as it has done on past occasions, including in the case of Libya.
“The application for arrest warrants is merely the beginning of a judicial process,” she wrote in a statement on Monday.
“The ICC has been a functioning court – it has seen convictions, acquittals, and dismissals, as we would expect from an impartial and non-political judicial body.”
It remains unclear whether any sanction efforts have yet gathered the support needed to advance through either the Republican-led House or the Democrat-controlled Senate.
White House Press Secretary Karine Jean-Pierre told reporters Tuesday that administration officials were discussing “next steps” with lawmakers.
Watching from across the world in Russia, Kremlin spokesman Dmitry Peskov told reporters that its adversary’s “attitude and willingness to use sanctions methods even against the ICC” was “more than curious”.