The timing and outlook for the president’s impeachment trial were already murky. In a pair of votes in December, the House impeached Mr. Trump for abuse of power and obstruction of Congress. The charges stem from his bid to pressure Ukraine to investigate his political rivals, while withholding nearly $400 million of military aid.

Ms. Pelosi has refused to transmit the charges against Mr. Trump to the Senate, in a bid to give Senate Democrats more leverage as they try to force Republicans to agree to call administration witnesses and gain access to more documents. The president blocked administration officials from testifying in the House inquiry and refused to turn over documents that impeachment investigators requested, prompting the obstruction charge.

Now, the question is whether the coming debate on Iran will affect the calculations by Democrats and Republicans strategizing over the terms and length of a trial.

Democrats on the left argue that the impulses that led Mr. Trump to strike General Suleimani are themselves grounds for his removal.

“The issues are connected,” said Representative Ro Khanna, Democrat of California, who sponsored legislation to block Mr. Trump from launching an unauthorized strike against Iran. “It shows the same reckless pattern of policymaking that he engaged in with Ukraine. It’s no longer a matter of standing up for the rule of law and the Constitution. This is a matter of safeguarding our national security and peace because a president that disregards constitutional processes can pose a huge risk to stability and peace.”

Senators spent the year-end holidays preparing for the impeachment trial, a showdown over the fate of Mr. Trump’s presidency that could consume parts of January and February.

Lawmakers and aides close to Ms. Pelosi say she has not yet made up her mind on how or when to proceed, and said foreign policy would not affect her thinking. A decision could come as soon as this week, when House lawmakers reconvene on Tuesday and the speaker holds a series of meetings with her leadership team.