President Michael D Higgins said the people of Ireland are indebted to the "courage, resolution and exemplary commitment" of Coast Guard members Captain Dara Fitzpatrick and her crew.
The President led tributes to the crew of Rescue Helicopter 116, which crashed off the coast of Mayo yesterday morning.
He said it marked a "dark day in the history of the Coast Guard" with a member of the service losing her life while providing assistance to others.
"On behalf of the people of Ireland, may I pay tribute to Captain Dara Fitzpatrick," he said.
"My thoughts are with her family at this difficult moment and also with the families of the missing crew.
"It is appropriate that we acknowledge and pay tribute to the efforts of her colleagues at the Coast Guard who have been working at a time which must be for them a time of great grief and uncertainty."
Taoiseach Enda Kenny extended the "deepest sympathy" of the Government to the family of Captain Fitzpatrick.
Speaking in Washington, Mr Kenny said he knows well the area of the Mayo coast where Rescue 116 went down.
"Obviously the search continues and on behalf of the Government again, we pay our respects to the family of Dara Fitzpatrick.
"Clearly in the analysis and investigation into this we want to uncover what exactly happened in respect of the lack of communications and loss of contact with Rescue Helicopter 116," Mr Kenny said.
He told reporters that he learned about the lack of communications from the rescue team late last night.
The Taoiseach has been briefed on the unfolding situation by Transport Minister Shane Ross and the Chief of Staff for the Defence Forces, Mark Mellet.
Mr Ross said his "heart goes out" to the loved ones of the victims, adding: "This is a terrible day."
In paying tribute to the captain of the aircraft, he said "no resources will be spared" in the search for the three remaining crew members.
"My thoughts and prayers are with the friends and families and colleagues of the four people on board," Mr Ross said.
"It is difficult to imagine what they must be feeling at present as they wait for word of their loved ones."
Housing Minister and avid sailor Simon Coveney admitted he was personally shocked by the tragedy.
"This is a very dark day for the emergency services," the Cork TD said. "These are incredibly professional people and they provide an amazing service. They have helped to prevent so many deaths and tragedies at sea."
A lifelong sailor and water sports enthusiast, Mr Coveney has been a major campaigner for marine safety.
Health Minister Simon Harris said the rescue workers epitomise "courage, bravery, selfishness and dedication of care".
Fianna Fáil leader Micheál Martin also expressed his deepest sympathy.
"Captain Dara Fitzpatrick died in the service of the State; doing the job she loved. I want to express my deepest condolences to her family on their loss," he said.
"This tragedy should remind us all that there are thousands of people putting their lives on the line every day on our behalf."