The Organisation of American States (OAS) decided on Friday night to send a high-level diplomatic delegation "as soon as possible" to investigate the situation and help "strengthen democracy".
After a meeting in Washington, the OAS announced its plan in a resolution that avoided explicit recognition of the government of newly sworn-in President Alfredo Palacio.
Gutierrez, seeking asylum in the Brazilian ambassador's residence, lashed out at opponents on Friday in his first public comments in three days, a recorded statement broadcast on Ecuadoran television that was apparently intended for supporters. He said Wednesday's congressional vote removing him from office was illegal.
"Through an unconstitutional decision, with 62 votes, and without (my) having abandoned the post, they have taken me out of the presidency," the ex-army colonel said, urging followers to relay his message across the country.
"I think there has to be justice, respect for democracy, the constitution, and I ask you to make these declarations," he said in the recording.
More than 200 protesters blocked the gates of the ambassador's residence on Friday night, demanding Gutierrez be tried for abuse of power, corruption and the repression of peaceful protests.
Waving flags, they chanted: "They won't move us!" "He's not getting out of here," said Marta Cecilia Puente, 38, who joined the protest with her 11-year-old son. "We'll stay until he's arrested."
When the Brazilian ambassador tried to leave, the crowd mobbed his sport-utility vehicle, banging on the hood and shaking the vehicle as riot police tried to keep them back. Unable to drive past, the vehicle slowly reversed back into the compound.
Ecuadoran Foreign Minister Antonio Parra said the government was in the process of arranging safe passage for Gutierrez, but he did not specify when. He said it was a very delicate matter and that no set timeframe for doing so existed.