Ferrari's Charles Leclerc and Red Bull's Max Verstappen say they will not take the knee before the season-opening Austrian Grand Prix.
But both have emphasised their support for the fight against racism.
They are the first two drivers to state their position on a topic that has caused controversy among the F1 drivers.
Leclerc said his decision was based on the fact that taking the knee "could be seen as controversial in some countries".
He added: "I believe what matters are facts and behaviours in our daily life rather than formal gestures.
"I will not take the knee but this does not mean at all that I am less committed than others in the fight against racism."
Verstappen said: "I am very committed to equality and the fight against racism. But I believe everyone has the right to express themself at a time and in a way that suits them.
"I will not take the knee today but respect and support the personal choices every driver makes."
The drivers issued a collective statement through the Grand Prix Drivers' Association on Saturday saying they "stand united with their teams against racism and prejudice, at the same time embracing the principles of diversity, equality and inclusion and supporting F1's commitment to these.
"Together the drivers will all show their public support for this cause on Sunday ahead of the race, recognising and respecting that each individual has the freedom to show their support for ending racism in their own way and will be free to choose how to do this."
Drivers' reluctance to take a knee shows 'lack of understanding' - Hamilton F1 drivers to wear 'end racism' T-shirts before Austrian Grand PrixBut some are uncomfortable with taking the knee, a gesture that originated in the NFL in the US to call attention to issues surrounding racial equality and police brutality, because of the political connotations the gesture carries in some countries.
World champion Lewis Hamilton said on Saturday that the reluctance was due to a lack of understanding of the issue of racism.
The Mercedes driver said he had made his point to the drivers at a meeting on Friday.
"I just described the scenario that silence is really generally complicit. There is some silence in some cases," said Hamilton, F1's only black driver.
"But I think it is part of a dialogue of people trying to understand because there are still some people who don't fully understand what is happening and what is the reason for these protests and I continue to try to be that guider and try to influence as many people as I can with it."
Red Bull's Max Verstappen has also tweeted that he will not take a knee before the grand prixAll the drivers are expected to wear T-shirts bearing the message 'end racism' before the race, and Hamilton has not yet said what other gestures he will make.
Renault's Daniel Ricciardo, who along with Leclerc was one of the drivers to speak out against racism on social media last month, said: "I've certainly been supportive of the Black Lives Matter movement. I've read a lot and tried to learn more about it. It's something which has certainly caught my interest and something I 100% want to support.
"The chat with the drivers was essentially this: all of us are 100% on board with supporting it and ending racism. None of us are 'anti' this. So we all support that.
"I think there was just a little bit of perhaps difficulty with some drivers and their nationality and what perhaps something like taking a knee would represent.
"Obviously the reasons why we will do it is purely to support Black Lives Matter; it's nothing political or anything else. But there is a little bit of a fine line, I think, with some drivers and their nationalities and how it's perceived.
"But we heard all of them, we heard everyone's opinion, and we're not going to try to do anything against or put anyone in jeopardy. We've all understood that we'll do what we feel comfortable with.
"No-one's going to be judged or criticised if they don't stand there in a certain way or take a knee. But I think the intention is for us to support it and we'll probably show that as a unit. And then if a few of us choose to do something extra, then that'll be the case."