Representative Frederica Wilson said he had told Myeshia Johnson: "He knew what he was signing up for, but I guess it hurts anyway."
Mr Trump said Ms Wilson's account was "totally fabricated".
Sgt La David Johnson was killed in Niger by Islamist militants this month.
He was one four US special service soldiers who died in an ambush.
Mr Trump had already been criticised for not contacting the families of the dead servicemen right after the fatal ambush on 4 October.
Sgt Johnson's mother, Cowanda Jones-Johnson, backed Representative Wilson's account of the phone call.
"President Trump did disrespect my son and my daughter and also me and my husband," she told the Washington Post newspaper.
A separate case which saw Mr Trump offer money to the grieving father of a dead serviceman in a call, but allegedly not pay up, has now emerged.
"He said: 'I'm going to write you a cheque out of my personal account for $25,000', and I was just floored," the father told the Washington Post.
The White House subsequently told the newspaper that the cheque had been sent, saying it was a "generous and sincere gesture".
What does Trump's accuser say?
Ms Wilson, who represents a Florida district, told CNN the president's call had been made shortly before Sgt Johnson's coffin arrived by aircraft in his home city of Miami.
Ms Wilson told WPLG, a Miami TV station, she had heard the president's "so insensitive" remarks to the widow on speakerphone in a limousine.
"To me, that is something that you can say in a conversation, but you shouldn't say that to a grieving widow," she said.
"And everyone knows when you go to war, you could possibly not come back alive. But you don't remind a grieving widow of that."
Ms Wilson told the Washington Post that Ms Johnson, who is expecting the couple's third child, had broken down in tears after the conversation.
"He made her cry," Ms Wilson said.
The congresswoman told the newspaper that she had wanted to grab the phone and "curse him out", but an army sergeant who was holding the handset would not let her speak to the president.
Ms Johnson responded to Mr Trump's denial by tweeting: "I still stand by my account of the call b/t @realDonaldTrump and Myeshia Johnson. That is her name, Mr Trump. Not "the woman" or "the wife".
She later issued a statement saying she did not wish to "engage in a petty war of words with Mr Trump" but again standing by everything she had said.
How did Trump respond?
The president tweeted on Wednesday morning: "Democrat Congresswoman totally fabricated what I said to the wife of a soldier who died in action (and I have proof). Sad!"
Mr Trump has yet to provide any evidence.
A White House official said Mr Trump's conversations with the families of dead servicemen were private.
Mr Trump later told reporters: "I did not say what she [Ms Wilson] said... I had a very nice conversation."
When asked about what "proof" he could offer, Mr Trump said: "Let her make her statement again, then you will find out."
Later, at a White House briefing, press secretary Sarah Sanders condemned Ms Wilson who she said had "politicised" the issue.
"This was a president who loves our country very much, who has the greatest level of respect for men and women in the uniform and wanted to call and offer condolences to the family.
"And I think to try and create something from that... is frankly appalling and disgusting."