Minnesota Senator Al Franken downplayed new sexual harassment claims against him in his apology Thursday.

The Democrat admitted in the statement he 'crossed a line' with some female acquaintances during 'greetings and embraces for a hug or photo.'

His accusers have claimed the politician touched their buttocks during events for his first campaign for Senate.

The women on condition of anonymity told Huffington Post the alleged events took place in Minneapolis back in 2007 and 2008.

'I've met tens of thousands of people and taken thousands of photographs, often in crowded and chaotic situations. I'm a warm person; I hug people,' Franken said.

'Some women have found my greetings or embraces for a hug or photo inappropriate, and I respect their feelings about that.'

In the statement he suggested he did not remember specific incidents at the events events, while adding 'it's difficult to respond to anonymous accusers.'

Sen. Al Franken admitted he 'crossed a line' after two new women came forward alleging Franken (pictured) touched their buttocks during events for his first campaign for Senate

The women said the events occurred in Minneapolis in 2007 and 2008. Last week Leann Tweeden (pictured), spoke out about a similar incident involving Franken that happened in 2006. Tweeden accused Franken of forcibly kissing her and putting his hands on her breasts

The former comedian expressed his regrets and assured to be 'much more careful' in future situations.

'I feel terribly that I've made some women feel badly and for that I am so sorry, and I want to make sure that never happens again,' he said.

The two new allegations are the third and fourth claims against Franken in the past week.

Last week, Franken was accused of forcibly kissing Leeann Tweeden while rehearsing for a 2006 USO tour.

Franken also was photographed with his hands over her breasts as she slept.

'I felt disgusted and violated,' she wrote on the website of her talk radio program.

Franken's initial statement noted that he did not remember the USO skit happening that way.

Lindsay Menz, 33, was the second woman to come forward, alleging Franken grabbed her buttocks during a photo op at the Minnesota State Fair.

One of the new victims, a 38-year-old book editor, told the Huffington Post that her story is similar to Menz's story.

'He grabbed my buttocks during a photo op,' the woman said, referring to the incident that allegedly took place on June 25, 2007.

Lensay Menz, (left) was the second woman to claim that Franken, (right) groped her when the two took this picture at the Minnesota State Fair in 2010

That incident reportedly took place at the Women's Political Caucus in Minneapolis.

The second victim to come forward this week told HuffPost that Franken cupped her butt with his hand during a 2008 Democratic fundraiser at the Loft Literary Center in Minneapolis.

She alleges he also suggested the two visit the bathroom together.

'I shook his hand, and he put his arm around my waist and held it there,' the second woman said. 'Then he moved it lower and cupped my butt.'

She added: 'I was completely mortified,' while speaking with HuffPost.

'My immediate reaction was disgust,' the second woman said. 'But my secondary reaction was disappointment. I was excited to be there and to meet him. And so to have that happen really deflated me. It felt like: 'Is this really the person who is going to be in a position of power to represent our community?''

Franken said he 'can categorically say that I did not proposition anyone to join me in any bathroom'.

Menz told CNN last week that the interaction with the Minnesota senator made her feel 'gross.' She said she immediately told her husband that Franken had 'grabbed' her bottom and that she posted about it on Facebook.

Her story followed Los Angeles broadcaster, Tweeden.

Senate Majority Leader Mitch McConnell has called for an ethics investigation of Franken, which Franken said he supports.