Tory leadership candidate Matt Hancock is understood to be considering pulling out of the race, as the remaining candidates consider how best to challenge frontrunner Boris Johnson.
BBC political editor Laura Kuenssberg said the health secretary could make a decision within hours, after getting 20 votes in the first ballot of Tory MPs.
That left him in sixth place in the race, well behind Mr Johnson on 114.
The top two left after further ballots will be voted on by party members.
Mr Johnson received more than double the number of votes of his nearest rival – Foreign Secretary Jeremy Hunt – putting him well on course to secure one of those two spots.
Three contenders – Mark Harper, Andrea Leadsom and Esther McVey – were knocked out of the contest on Thursday.
But it is not yet clear which candidate their supporters will now give their votes to instead.
The former London mayor and foreign secretary said he was “delighted” to win the opening battle but warned that his campaign still had “a long way to go”.
The seven remaining candidates progress to the next round of voting next Tuesday, unless any of them choose to withdraw between now and then.
Laura Kuenssberg said discussions were now “live between other camps in the race” over what to do next and whether there should be an effort to come together behind one candidate who could beat Mr Johnson.
Speaking after the results were announced, Mr Hunt said: “Boris did well today but what the result shows is, when it comes to the members’ stage, I’m the man to take him on.”
Further ballots are scheduled to take place on 18, 19 and 20 June to whittle down the contenders until only two are left.
The final pair will then be put to a vote of members of the wider Conservative Party from 22 June, with the winner expected to be announced about four weeks later.
Meanwhile all of Mr Johnson’s remaining rivals have signed a joint letter committing to taking part in televised leadership debates on Sunday, in an apparent bid to put pressure on Mr Johnson, who has not committed to do so.
Sources close to Mr Johnson say they are still in discussions with broadcasters
Work and Pensions Secretary Amber Rudd, who is backing Mr Hunt, urged them to appear, saying the Conservative Party “needs to remember that we’re not just choosing a leader, we’re choosing a prime minister and the public need to see them”.
And former Brexit secretary David Davis, who is backing Mr Raab, said it was “very important” for the public to hear from the contenders.
Mr Johnson has previously been criticised by some of his rivals for not taking part in media interviews during the campaign.
The leadership race has so far been dominated by Brexit and arguments over whether a deal can be renegotiated with the EU by 31 October, and whether talking up a no-deal Brexit is a plausible promise.
The UK’s next prime minister
On Tuesday 18 June BBC One will host a live election debate between the Conservative MPs still in the race.
If you would like to ask the candidates a question live on air, use the form below. It should be open to all of them, not a specific politician.