Representative Andre Carson said he was also planning a broader bill that would require the US government to investigate any killing of US journalists overseas.
A group of lawmakers sought to force a US-led probe into the killing of Palestinian-American journalist Shireen Abu Akleh after her family failed to win a commitment from President Joe Biden.
In response, members of Congress on Thursday said they were introducing a bill that would authorise an investigation backed by US intelligence.
"We are urging our colleagues to see this as a free press issue. To put aside Israeli and Palestinian politics and see this for what it is: an attack on independent reporting and the killing of our citizen," Representative Andre Carson told reporters, with her relatives by his side.
He said he was also planning a broader bill that would require the US government to investigate any killing of US journalists overseas.
Relatives of the prominent Al Jazeera journalist who was shot on May 11 while covering an Israeli operation in the West Bank and held US citizenship were invited to Washington to see Secretary of State Antony Blinken after unsuccessfully seeking a meeting with Biden on his recent trip to the Middle Eastern region.
Blinken in the meeting on Tuesday offered condolences and promised to seek "accountability," but the family said he did not commit to their requests to launch a US-led investigation.
The State Department, examining Israeli and Palestinian probes, said on July 4 that Abu Akleh was likely killed by Israeli fire but that there was no evidence she was intentionally targeted and that the bullet was too damaged for a conclusive finding.
Israel denies it
Israel strongly denies it would target a journalist and says it is continuing its own investigation.
Representative Marie Newman sharply criticised the State Department for not acting already.
"I am embarrassed and outraged and incensed that there is no investigation, and I'm going to call the State Department out for dragging their feet," she said.
The lawmakers acknowledged they faced odds on their legislation, with an earlier attempt to require an investigation through an amendment in a broad defence bill failing.
"Maybe for some of my colleagues, if they need to take out the word Palestinian from Palestinian-American for her life to matter, they would actually support it," said Representative Rashida Tlaib, who is of Palestinian descent.