WASHINGTON — Secretary of State Mike Pompeo refused to tell Congress on Tuesday what the United States would do if the Israeli government tried to annex the West Bank, as Prime Minister Benjamin Netanyahu recently promised to do if re-elected.

Mr. Pompeo’s silence on the issue is a break from the actions of previous administrations. Senior American officials have long and explicitly discouraged any formal attempt by Israel to extend sovereignty over some or all of the disputed territory of the West Bank and its population of 2.6 million Palestinians.

In a last-minute bid to win votes in Tuesday’s neck-and-neck Israeli elections, the conservative Mr. Netanyahu said in a weekend interview that he would “apply sovereignty” to some or all of the West Bank. Mr. Netanyahu has hinted that he would get a nod for any such action from President Trump, who last month recognized Israeli sovereignty over the disputed Golan Heights and earlier moved the American Embassy from Tel Aviv to Jerusalem, a contested city.

Mr. Pompeo appeared Tuesday afternoon at a hearing of a Senate Appropriations subcommittee to discuss the Trump administration’s 2020 budget request for the State Department and the primary United States aid agency. Last month, Republican and Democratic members of the House criticized the budget that proposed cutting State Department funding by more than 23 percent.