US Senate Majority leader Mitch McConnell has abruptly backed off some of his proposed rules for President Donald Trump’s impeachment trial, easing plans for a tight two-day schedule and agreeing that House evidence will be included.

He acted after protests from senators, including fellow Republicans.

The trial quickly burst into a partisan fight at the Capitol as the president’s lawyers opened arguments on Tuesday in support of Mr McConnell’s plan.

Democrats objected loudly to Mr McConnell’s initially proposed rules, and some Republicans made their concerns known in private.

Without comment, the Republican leader quietly submitted an amended proposal for the record, after meeting behind closed doors with senators as the trial opened.

The handwritten changes would add an extra day for each side’s opening arguments and stipulate that evidence from the Democratic House’s impeachment hearings be included in the record.

There is still deep disagreement about calling additional witnesses.

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White House counsel Pat Cipollone during the impeachment trial in the Senate (Senate Television via AP)

“It’s time to start with this trial,” said White House counsel Pat Cipollone, the president’s lead lawyer as the proceedings opened in public.

Chief Justice John Roberts gavelled open the session, senators having taken an oath last week to do “impartial justice” as jurors.

House prosecutors were on one side, Mr Trump’s team on the other, in the well of the Senate, as senators sat silent at their desks, no mobile phones or other electronics allowed.

Senators were stunned by Mr McConnell’s shift, which came during the private lunch and briefly delayed the start of the historic session.

A spokeswoman for Republican Senator Susan Collins said that she and others had raised concerns.

The Maine senator sees the changes as significant improvements, said spokeswoman Annie Clark.

Senate Democratic leader Chuck Schumer was to offer the first amendment to the rules — a proposal to issue a subpoena to the White House for “all documents, communications and other records” relating to the Ukraine matter.

It seeks records about Mr Trump’s orders to hold off military aid to Ukraine, along with White House communications about any investigations it wanted about the Democratic rival Joe Biden and his son.

In a vote later, it was likely to be rejected by Republicans.

Democrats had warned that the rules package from Mr Trump’s ally, the Senate Republican leader, could force midnight sessions that would keep most Americans in the dark and create a sham proceeding.

“This is not a process for a fair trial, this is the process for a rigged trial” Representative Adam Schiff, the chairman of the House Intelligence Committee leading the prosecution, told reporters.

He called it a “cover-up”.

Mr Schiff opened his arguments before the Senate playing a video of Mr Trump calling for more witnesses to testify.

Mr Schiff noted the sudden change in proposed rules, made moments before he spoke.

“The facts will come out in the end,” Mr Schiff said. “The question is, will it come out in time?”

Mr McConnell said, “The president’s lawyers will finally receive a level playing field,” contrasting it with the House impeachment inquiry.

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Donald Trump after attemding session at the World Economic Forum in Davos, Switzerland (Markus Schreiber/AP)

The rare impeachment trial, unfolding in an election year, is testing whether Mr Trump’s actions toward Ukraine warrant removal at the same time that voters are forming their own verdict his White House.

Mr Trump himself, in Davos, Switzerland, for an economic conference, denounced the proceedings as “a total hoax”, and said, “I’m sure it’s going to work out fine.”

With Mr Trump’s presidency on the line, and the nation deeply divided just weeks before the first Democratic primary contests, four senators who are also presidential candidates will be off the campaign trail, seated as jurors.

“My focus is going to be on impeachment,” Senator Bernie Sanders, the Vermont independent running for the Democratic nomination, told reporters.

He said his supporters would keep working “to defeat the most dangerous president in American history.”