By Luc Cohen and Jody Godoy

NEW YORK (Reuters) -Donald Trump's lawyer sought to show inconsistencies in porn star Stormy Daniels' various tellings of a 2006 sexual encounter she has said she had with Trump, part of an effort on Thursday to undermine her credibility as a witness in the first criminal trial of a sitting or former U.S. president.

Her unflattering account of a sexual encounter with Trump in a Lake Tahoe hotel suite while he was married to his wife Melania riveted jurors on Tuesday and reminded U.S. voters of some of the more lurid aspects of his 2017-2021 presidency as he campaigns to win back the White House this year.

Facing questioning on Thursday by defense lawyer Susan Necheles in a Manhattan courtroom, Daniels stuck to her account.

"You're trying to make me say that it changed, but it hasn't changed," Daniels told Necheles.

Trump, 77, has pleaded not guilty to 34 counts of falsifying business records to cover up his former lawyer and fixer Michael Cohen's $130,000 payment to Daniels, 45, for her silence ahead of the 2016 U.S. presidential election about the alleged encounter. Trump has denied ever having sex with Daniels.

Trump, the Republican candidate challenging Democratic President Joe Biden in the Nov. 5 U.S. election, has called the trial a politically motivated attempt to undermine his campaign.

Prosecutors have said Trump's efforts to obscure the paper trail for the payment to Daniels corrupted the 2016 election in which he defeated Democrat Hillary Clinton by preventing voters from learning about a story that might have swayed their vote. 

After testimony ended on Thursday, Trump lawyer Todd Blanche once again asked Justice Juan Merchan to declare a mistrial on the basis of Daniels' testimony.

Blanche argued that her detailed testimony about the alleged sexual encounter, including her statement that Trump was not wearing a condom, had veered into territory that was irrelevant to the case and would prejudice jurors against Trump.  

"This is not a case about sex," Blanche said. "This is not a case about whether that incident took place or didn't take place."

Merchan denied the request, saying that because Blanche had argued in his opening statement on April 22 that the encounter never happened prosecutors were allowed to try to rehabilitate Daniels' credibility.

"Your denial puts the jury in a position of having to choose who they believe," Merchan said. 

The judge also denied a similar request on Tuesday. 

In addition, Blanche requested that a gag order restricting Trump's public comments about jurors and witnesses be loosened to let the defendant publicly respond to questions about Daniels' testimony. Merchan also denied that request, stating that other witnesses may see Trump's comments and become concerned that he would say similar things about them. 

Christopher Conroy, a prosecutor, suggested that the proper way for Trump to respond to Daniels would be to testify in his own defense. Trump before the trial told reporters he would testify, though it remains to be seen whether he will do so.

"There is a proceeding here that this (gag) order is designed to protect," Conroy said. "If somebody wants to respond to something that's said in this room, that can happen in this room."

The judge has fined Trump $10,000 for running afoul of the gag order 10 times, and said further violations could land him in jail.

DEFENSE SAYS DANIELS 'MADE ALL THIS UP'

In nearly four hours of cross-examination on Tuesday and Thursday, Necheles asked Daniels about her earlier testimony of the alleged encounter compared with versions in a book she wrote and interviews she gave over the years.

She asked Daniels why in a 2018 interview to Vogue magazine she did not mention that Trump's bodyguard had been outside the hotel room where the encounter happened. Daniels on Tuesday had testified that her awareness of the bodyguard's presence contributed to a power imbalance with Trump that left her feeling uncomfortable.

"You made all this up, right?" Necheles asked Daniels at one point.

"No," Daniels said emphatically, sitting with her hands folded and legs crossed. 

Just before ending the cross-examination, Necheles asked Daniels if she had knowledge of Trump's business records - part of an effort to paint her testimony as irrelevant to the false business records charges at hand. 

"I know nothing about his business records, no," Daniels said. "Why would I?" 

Daniels completed her testimony, with a combined seven hours on the witness stand over two days.

Former Trump White House aide Madeline Westerhout took the witness stand on Thursday afternoon and told jurors about checks he signed while in office. Westerhout is expected to return to the witness stand on Friday. 

This is the first of four criminal cases against Trump to go to trial. He has pleaded not guilty in all of them.