The first arrivals since Russia's war began were shown wearing bright yellow suits with blue trimmings.
They were warmly welcomed on board, hugging and greeting their fellow American, Russian and German crew.
"Sometimes yellow is just yellow," said the Roscosmos space agency.
The ISS is a joint project between Russia, America, Canada, Japan and several European countries.
It is led by a US-Russian partnership that has continued for two decades despite fluctuating tensions between the two world powers.
Russian cosmonauts Denis Matveyev, Oleg Artemyev and Sergey Korsakov docked at the ISS after a three-hour flight which blasted off from a Russian-owned facility in Kazakhstan.
"Congratulations on the successful docking," a voice from Russia's mission control said.
A few hours later, two sets of hatches were opened and the three smiling men floated into the space station one by one in their yellow suits.
The standard-issue Russian uniform is plain blue, and at least one of the men was seen wearing this before take-off.
The moment was live-streamed by both Roscosmos and Nasa, the American space agency.
"It became our turn to pick a colour," Mr Artemyev said when he was asked about the suits in a live-streamed press conference.
"We had accumulated a lot of yellow material so we needed to use it," he joked. "That's why we had to wear yellow."
Since the invasion of Ukraine, people around the world have used the colours of its national flag to show solidarity and support.
But Roscosmos's press service dismissed the reports as a "funny invention" by foreign bloggers and media.
"The flight suits of the new crew are made in the colours of the emblem of the Bauman Moscow State Technical University, which all three cosmonauts graduated from... To see the Ukrainian flag everywhere and in everything is crazy."
The head of Roscosmos, Dmitry Rogozin, is a strong supporter of the invasion and he suggested the claims that the cosmonauts were wearing Ukrainian colours had come from Ukrainian nationalists.
Roscosmos later published another picture of Oleg Artemyev wearing an obviously Russian suit.
The three Russians will begin a science mission on the ISS that is set to last just over six months.
They will replace three current crew members who are scheduled to fly back to Earth on 30 March.
The colours certainly speak to the moment, but what is the real motivation in wearing them? Does it signal support for Ukraine or the opposite? After all, the suits do display Russian flags.
Perhaps neither view is correct.
It has been suggested that the colours are a reflection of the fact that all three cosmonauts attended the Bauman Moscow State Technical University which has a similar colour scheme. It's a "Bauman crew", the university has been trumpeting.
The cosmonauts themselves, however, said noticeably little.
What we do know is that 400km (248 miles) above the Earth, East and West have no choice but to continue friendly relations.
While space co-operation is falling apart elsewhere - witness the ExoMars rover, for example - on the ISS the partners are joined at the hip. Russia provides the propulsion for the station, the Americans provide the power. The ISS cannot exist without either party.