The second woman to allege that she was pressured into having an abortion by Herschel Walker, the Republican nominee in Georgia’s hotly contested US Senate race, on Tuesday presented previously unseen letters, audio recordings and pages of her personal diary that she said were evidence of their relationship, which he has denied.

At a press conference in Los Angeles organized by her lawyer, Gloria Allred, the anonymous woman known only as Jane Doe came forward anew with a raft of fresh materials. She said she was doing so because when she first aired her allegations last month “and told the truth, he denied that he knew that I existed”.

The alleged new evidence of the relationship between the woman and the former college football star included a voicemail recording in which Walker was purported to say to her: “This is your stud farm calling, you big sex puppy you”.

Jane Doe also read out a letter which she said had been written by Walker to her parents. “I do love your daughter and I’m not out to hurt her. She has been a strong backbone for me through all of this,” the letter said.

The new allegations surfaced just as early voting is set to begin in the important run-off election for a Georgia seat in the US Senate between Walker, who has publicly called for abortion to be banned, and the Democratic incumbent, Raphael Warnock, following a neck-and-neck result in the midterm elections.

Asked whether she was coming forward with a new round of allegations in order to influence the election, Jane Doe said: “Voters can make their own decision. All I can do is tell the truth.”

The unnamed woman initially raised her claims on 26 October that she was pressured into an abortion. She alleged that she had an intimate relationship with Walker for six years while he was playing for the Dallas Cowboys and that he paid for her to have an abortion in 1993, driving her to the clinic.

Walker rebutted the claims, saying: “I’m done with this foolishness. I’ve already told people this is a lie and I’m not going to entertain it.”

At Tuesday’s press conference, Jane Doe read passages of what she said were her personal diaries from 1993 in the days immediately after she learnt she was pregnant. In one extract Walker is alleged to have told her that the pregnancy was “probably his ‘fault’ since he had very high levels of testosterone”.

In a second passage, she wrote that Walker “has about gone off the deep end over this whole thing … He thinks that by not having the baby we do have a future chance for happiness that we can ‘grow strong again together’.”

Allred read out what she said was a signed declaration from a friend of Jane Doe’s in which she recalled her confiding to her in 1993 that she was pregnant and that Walker had been the partner. Several years later, the friend said in her declaration, “she confessed to me that she had in fact had an abortion in 1993” and that Walker had personally driven her to the clinic.

The first woman to make allegations against Walker told the Daily Beast last month that he paid for her to have an abortion in 2009.