He was speaking in the first leaders' debate of the Irish general election.
He was responding to Fianna Fáil's Micheál Martin who said he would not form a coalition with Sinn Féin as he does not trust them on security.
He said: "Politicians here could learn a lesson from the unionists, who have more reason to distrust Sinn Féin."
Mr Adams referred to past and present leaders of the Democratic Unionist Party (DUP), who have led a power-sharing government with Sinn Féin in Northern Ireland since 2007.
"Ian Paisley can go into government with Martin McGuinness, and Peter Robinson can go into government, and Arlene Foster can go into government with Martin McGuinness," Mr Adams said.
The Sinn Féin leader was challenged by one of the debate moderators, Pat Kenny, that the D'Hondt system forces the parties in Northern Ireland together.
The D'Hondt system is a type of proportional representation used to allocate seats and ministerial posts.
Mr Adams said it was the citizens of Northern Ireland make the decisions about who goes into government by them giving a mandate.
Taoiseach Enda Kenny was asked whether the bookmakers' predicted outcome, a Fine Gael/Fianna Fáil coalition, was the most likely outcome.
He replied that voters have a choice between "the party that wrecked the country, or two parties with different perspectives who have worked together to set the country on the path to recovery". He said Fine Gael/Labour will provide stability.
When the debate moved to the Irish economy, Labour leader Joan Burton accused Sinn Féin of "fuzzy economics" which would kill jobs.
The Irish deputy prime minister said she is mystified by Sinn Féin's plans to cut the Universal Social Charge (USC), claiming it would reduce tax only for people earning less than €20,000 (£15,515).
USC is a tax that was introduced in December 2010 as a temporary measure by the late finance minister, Brian Lenihan.
It was applicable to all gross incomes over €4,004 (£3,106)
Still on the issue of taxation, Mr Kenny said Sinn Féin would impose a 65% marginal tax rate and "wreck the economy".
Meanwhile, Fianna Fáil leader Micheál Martin claimed Fine Gael would bring in US-style tax rates and run down public services.
Ms Burton said low and middle income families need to "see the back of the USC", which Fianna Fáil brought in.
Analysis - Colletta Smith
Amidst the shouts and accusations in the first leaders debate of this Irish election, the Sinn Féin leader gave some high praise to an unlikely party.
Mr Adam's praise for the leadership of the DUP comes days after Northern Ireland First Minister Arlene Foster told the BBC's Spotlight programme of the personal difficulty she found in working with Deputy First Minister Martin McGuinness.
Mr McGuinness spoke at the funeral of the man that Mrs Foster believes tried to kill her father.
She concluded her comments by saying that she would work with the deputy first minister because "the past is the past".
Fianna Fáil leader Micheál Martin has been keen to distance his party from the possibility of a coalition tie-up with Sinn Féin in the Republic of Ireland.
The issue of coalition partnerships is a hot political topic as it is unlikely that one party will win an outright majority in the upcoming Irish election.
The vote takes place on 26 February.
Sinn Féin leader Gerry Adams has told his political rivals in the Republic of Ireland they could "learn a lesson" from unionists in Northern Ireland.