CCTV footage of the push and the initial appeal attracted hundreds of calls from the public after being widely shared on social media.
41-year-old Eric Bellquist, a US citizen, was questioned by police but denies any involvement.
Mr Bellquist had denied being the man involved and claimed that he was in the USA at the time of the incident.
He was released on the same day pending further inquiries.
The 33-year-old victim was walking across Putney Bridge at about 7.40am on 5 May, when the incident occurred. Mat Knowles, the investigating officer from the Putney Safer Neighborhood Team, said in a statement. As the bus came to a stop, passengers got off to help her.
"Enquiries continue to identify the jogger who pushed the female pedestrian into the road".
The woman was put in "extreme" danger and only avoided a passing double-decker bus because of the quick reactions of its driver, police said.
Police have renewed their search for the jogger, described as a white man aged early to mid 30s, with brown eyes and short brown hair.
The Metropolitan Police says about 15 minutes later the runner returned in the other direction across the bridge, but when the woman attempted to speak to him, he "did not acknowledge her".
Trump warns North Korea against attacking Guam
He continued, "We're going to do a great job for you". "I just wanted to pay my respects, and we are with you 1,000 percent". In response, President Donald Trump has warned North Korea repeatedly that if it takes such action, the USA will hit back.
Toshiba moves closer to avoiding delisting
That would have reduced its ability to raise money for its cash-hungry memory chip business, risking its competitiveness. While agreeing generally with the financial results of Toshiba , the sign off from PwC did come with a caveat.