Ukrainian Ambassador Yevheniia Filipenko was among the numerous diplomats who filed out as the video began playing, leaving the room almost empty.
Outside they gathered in front of a Ukrainian flag and broke into strong applause that could be heard in the chamber where Lavrov's speech continued, with only a handful of ambassadors from countries including Yemen, Syria, Venezuela and Tunisia remaining to hear him.
"It is important to show a gesture of solidarity with our Ukrainian friends," said French ambassador Yann Hwang.
Russia has become an international pariah since launching a full-scale invasion six days ago.
At the same meeting, Ukraine's foreign minister accused Russia of war crimes through its shelling of his country and called for a special meeting to address Russian aggression and weapons of mass destruction.
"Russian indiscriminate attacks on civilian and critical infrastructure are war crimes and violations of the Rome Statute," Ukraine's foreign minister told the disarmament meeting before Lavrov spoke.
"Russian aggression is a global threat," he warned, insisting that "the response too must be global."
Earlier in the session, the president organised a minute of silence for the victims of fighting in Ukraine.