Senate Rules and Administration Chairman Richard C. Shelby gave a cool reception Thursday to a bipartisan draft bill disclosed the same day that would require large online platforms to collect and disclose data about the buyers of political advertising.

“We will look at everything; right now, a lot of that is being investigated,” the Alabama Republican said about a proposal from Democratic Sens. Mark Warner of Virginia and Amy Klobuchar of Minnesota and co-sponsored by Republican Sen. John McCain of Arizona. Asked whether he would be open to backing the bill in the future or other legislation to deal with the issue, Shelby said, “Not yet.”

The legislation is aimed at addressing the Russian advertising on Facebook during the 2016 presidential campaign and concern about Moscow’s meddling in the election. Shelby’s committee would have jurisdiction.

Other Republicans offered a measured response to the proposal outlined by Warner and Klobuchar in a news conference Thursday.

Sens. Cory Gardner of Colorado, chairman of the National Republican Senatorial Committee, and Deb Fischer, a member of Senate Rules and Administration, said they were open to the proposal.

“It needs to have a debate. It needs to have a hearing. Let’s figure out what’s right,” Gardner said.

But key Republicans including Senate Majority Leader Mitch McConnell, a member of Shelby’s panel and an arch foe of a 2002 campaign finance law, often resisted expansion of campaign spending restrictions in the past.

Klobuchar said she doesn’t have a green light for the bill to be discussed or marked up by the panel. “That will be very hard to have … unless Sen. Shelby agrees to have a hearing,” she said after Thursday’s news conference.

The draft bill would expand a provision in the 2002 campaign finance law to include “qualified Internet or paid digital communication” in the definition of electioneering communication, which now includes political advertising on television, radio and satellite communications. The measure would require online platforms with armies of users to keep a so-called public file — just like operators of television, radio and satellite communications currently — on the buyers of political advertisements, including names of persons buying the ads, the average rate charged and other information, such as a candidate name or a national legislative issue that is mentioned.

It would require online platforms with at least 50 million unique monthly “United States visitors or users” for a majority of the preceding 12 months to maintain a public file of electioneering communications purchased by a person or group spending more than $500 annually on ads on that platform. Proponents said the threshold was designed to skip over purchasers of just a few online ads, which might cost a few dollars, and only capture bulk purchasers.

The measure was praised by several watchdog groups.

Karen Hobert Flynn, president of Common Cause, a nonpartisan group that monitors elections and campaign finance, called the proposal “a critical step forward in enhancing the transparency of online political advertising.”

Lawrence Noble, senior director and general counsel of the Campaign Legal Center, a nonpartisan research and litigation group specializing in elections, praised language in the bill that would require online platforms to make all reasonable efforts to ensure that foreign individuals and entities aren’t buying political advertising to influence American voters.

Noble said the language would provide data that could be used by candidates, parties or even private individuals to investigate suspicious ads. He said the proposal would keep in place the allowance for charities such as so-called 501(c)(4) groups to keep donors confidential, a provision that would enable groups to receive foreign funds and use it to buy political advertising without identifying the foreign donors.

“If questions arise about whether the 501(c)(4) is a front for foreign funding, that’s another issue,” said Noble, former general counsel of the Federal Election Commission. “But this bill provides a tool — with the public file — to at least know who is buying the ad and so you can begin to look into any allegations that the buyer is a front for foreign money.”

The bill drew a cautious response from industry groups.

“We are reviewing the legislation and look forward to further engagement with the sponsors,” said Michael Beckerman, president of the Internet Association, in a written statement. The group represents Google, Facebook and other online businesses.

“This is an important issue that deserves attention and the internet industry is working with legislators in both the House and Senate interested in political advertising legislation,” Beckerman said.