"Yes, I am running for a second mandate," Lagarde told France 2 television from the Davos economic forum on Friday, pointing to the support she had already received before officially announcing her candidacy.
British Finance Minister George Osborne on Thursday tweeted that he was "delighted to nominate" her for a new term and Germany's finance ministry said she had been a "far-sighted and successful crisis manager in difficult times".
Speaking at Davos this week US Treasury Secretary Jacob Lew said she had "done a great job", although Washington has not nominated her yet.
Lagarde, who has headed the IMF during the eurozone crisis, told France 2 that the United States usually waits until the end of the election process before backing a candidate but pointed to recent expressions of support.
"The words of the US Vice President [Joe Biden] the other day in his public intervention were very glowing - almost embarrassing - and the treasury secretary has said he hopes to enjoy working with me," she told France 2. "I think it is difficult for the United States to do much more this stage."
Lagarde's term ends in July and the IMF formally began accepting nominations on Thursday.
No other names have yet been raised but nominations remain open until 10 February and its executive board plans to make a decision by 3 March.
Lagarde has said she will fight the trial order and the IMF board has declared its confidence in her.
She easily won the contest to lead the world financial body in 2011, despite criticisms that Europeans have had a monopoly on the post since the IMF was established in 1944.
Lagarde also told France 2 that it was "imperative" that France continue its economic reforms.
The IMF on Tuesday lowered its forecast for the country's growth in 2016 0.2 points to 1.3 per cent.