WASHINGTON — Secretary of State Rex W. Tillerson was subjected to a full day of rough, bipartisan criticism on Tuesday as senators from both parties denounced the Trump administration’s plans to cut the State Department’s budget by about 30 percent.

Senators repeatedly asked whether issues such as the promotion of human rights, the protection of democracy, the campaign against human trafficking or efforts to halt the spread of nuclear weapons were priorities for the administration.

Mr. Tillerson assured the lawmakers that they were. But Republican and Democratic senators pressed a fundamental question: How can the Trump administration say it champions those efforts if it is cutting budgets for a range of important diplomatic initiatives — and eliminating others outright?

Each time, Mr. Tillerson patiently answered that priorities should not be judged only by dollars spent.