The phrase "affirm their support" is correct and usable in written English.
It can be used when expressing or confirming someone's backing or endorsement of a person, idea, or initiative.
Example: "The committee decided to affirm their support for the new policy during the meeting."
Alternatives: "confirm their backing" or "reiterate their support."
Republicans nationwide have recently made overtures to the gay groups to affirm their support for diversity.
We call on universities and other organisations to stand up to attempts at intimidation and affirm their support for the basic principles of democratic political exchange.
A squeeze seems likely, for those who would vote Tory can affirm their support for Simon Hayes, an independent candidate but a former Conservative councillor and chair of Hampshire Crimestoppers.
As he attacked the plan, Czech and Polish ministers met in Prague to affirm their support for the installations and send a signal to the Obama administration, pleading for it to go ahead.
"This presentation of the American flag is a very appropriate method for the N.F.L. clubs and players to affirm their support for the men and women of our Armed Forces on duty in Saudi Arabia and the Persian Gulf," Commissioner Paul Tagliabue said yesterday.
Back in late March, he was one of several Democrats to publicly affirm their support for gay marriage.
The White House and the Senate majority leader, Harry Reid, Democrat of Nevada, affirmed their support for Mr. Daschle.
Representatives from Britain, France and Italy all issued statements affirming their support for the NATO coalition's fight against the Taliban.
The two Democratic leaders in Congress, Senator Tom Daschle and Representative Richard A. Gephardt, issued a statement affirming their support for Mr. Gore.
Both candidates again affirmed their support for the notion that Egypt's laws apply from Islamic principles, but then the emphasis in their answers sharply diverged.
Long-term unemployment remained a significant concern, but voters affirmed their support for Borisov when they elected GERB candidate Rosen Plevneliev president in October 2011.
