The White House said the talks would take place on Tuesday.
The prosecutors played old videos in which two of the president's closest defenders said that abuse of power is a clear impeachable offense.
The Democratic lawmaker described how Trump solicited foreign interference in US elections, "abusing the powers of his office."
House impeachment managers led by veteran prosecutor Adam Schiff used the opening debate over trial procedures.
Greta Thunberg was in the audience in the Swiss Alps to hear the typically bullish speech by Trump.
In Washington, the Senate was about to enter the heart of the impeachment trial threatening his presidency.
Trump is accused of trying to pressure Ukraine into interfering in the 2020 US election to help him win, and then tried to thwart a congressional probe.
Business leaders will be keen to tout their awareness on climate change but are likely also to be concerned by the state of the global economy.
The meetings will take place on the sidelines of the Davos conference, which this year is focusing heavily on climate emergency and social inequality.
The "phase one" deal marks a truce in the two countries' trade war after nearly two years of tensions.
Apart from last week's blip caused by the US assassination of Iran's top general, markets have enjoyed a strong start to the new decade.
Trump is so confident that his Republican party majority will stay loyal that he sees no risk in jetting to Switzerland for the annual World Economic Forum.
Supreme Court Chief Justice John Roberts will deliver oath to the 100 senators and preside over the third impeachment trial of a chief in US history.
The US-China trade agreement lowers tensions between the two and provides a major boost to the global outlook.
Preparations will get underway for an impeachment trial that will open on Tuesday, January 21.
McConnell said he expected the House of Representatives to deliver the articles of impeachment against Trump to the upper chamber on Wednesday.
Analysts warned there will not likely be much more progress on the next phase of talks ahead of the November US presidential election.
The trade truce has boosted stock markets worldwide in recent days, as it takes the threat of new tariffs off the table for now.
The President and the first lady were met with chants of "four more years" and "U.S.A.!" as they waved to the crowd.
Asia was given a firm lead from Wall Street, where all three main indexes ended higher.
Once the House forwards the charges, the Senate has to begin trial proceedings within one day.
In an interview, US Defense Secretary Mark Esper said Trump was still willing to hold talks with Iran's leaders.