Mr. Schiff, speaking on CNN’s “State of the Union,” said impeachment “may be the only remedy” if Mr. Trump did in fact withhold aid to Ukraine in the hopes that the country would pursue an investigation into the Biden family. “The president is pushing us down this road,” he said. “We may very well have crossed the Rubicon here.”

Senator Christopher S. Murphy, Democrat of Connecticut, said Congress had to take action. “If we do have the evidence from this whistle-blower that the president indeed did try to bully a foreign power into affecting our elections, then we have to do something about it,” he said on “Meet the Press” on NBC as he called for release of the whistle-blower’s complaint.

Mr. Murphy, who recently visited Ukraine, said Mr. Zelensky expressed consternation to him that the security aid was held up. The senator said administration officials gave him two explanations for holding up the money — that Mr. Trump was concerned about corruption in Ukraine and that he thought Europe should be the one to assist Kiev rather than the United States.

But Mr. Murphy cast doubt on those explanations and said the situation was clearly suspicious. “Obviously, the timing of this looks really terrible,” he said.

While most Republicans remained silent, one prominent senator added his voice to the chorus of concern. “If the President asked or pressured Ukraine’s president to investigate his political rival, either directly or through his personal attorney, it would be troubling in the extreme,” Senator Mitt Romney of Utah wrote on Twitter on Sunday. “Critical for the facts to come out.”

In Kiev, Mr. Zelensky has not commented on the matter since the issue erupted in news reports in recent days, but Ukraine’s foreign minister, Vadym Prystaiko, was quoted telling a Ukrainian news outlet on Saturday that the country’s leaders did not take Mr. Trump’s phone call as pressure.