Trump's lawyer Rudy Giuliani told Fox News that it would be wrong for Mr Trump to concede because: "There is strong evidence that this was an election that in at least three or four states, and possibly 10, it was stolen."
The Trump campaign is yet to provide this "strong evidence".
Giuliani says further lawsuits will be filed over a lack of access for poll watchers in the state.
The president's campaign has said it will request a recount in Wisconsin "based on abnormalities seen" on election day, although this wouldn't require a lawsuit.
It's unclear when this recount would take place, since typically these don't happen until after officials finish reviewing the votes. The state's deadline for this part of the process is 17 November.
The Nevada Republican Party tweeted saying: "Thousands of individuals have been identified who appear to have violated the law by casting ballots after they moved from Nevada."
The case is focused on voters in Clark County, but the county's registrar has said: "We are not aware of any improper ballots that are being processed."
The Trump campaign filed a lawsuit in Arizona on Saturday, claiming some legal votes were rejected.
The case cites declarations by some poll watchers and two voters who claim they had problems with voting machines.
The lawsuit is under review, but Arizona's Secretary of State said it was "grasping at straws".