The phrase 'reiterate their commitment' is correct and usable in written English.
You can use it when someone has previously made a promise or commitment, and then wants to make sure that their commitment is clear and understood by repeating it. For example: The politician reiterated their commitment to improving the economy.
"The parties reiterate their commitment to resolve peacefully the final status of Abyei," the agreement said.
Surely our own farmers, who have worked for decades to stricter EU standards shaped by consumers' demand for safe, natural food, would reiterate their commitment to keeping them?
Instead, the leaders looked set to reiterate their commitment to longer-term structural measures like deepening Europe's 500 million-person single market to new areas like services and e-commerce.
The easy part will be where UK delegates reiterate their commitment to an open and competitive Europe, highlighting the vital national interest in the single market, destination for half of all British exports.
Following the state opening of parliament on Wednesday, ministers were busily touring the broadcasting studios doing their best to reiterate their commitment to continuing cross-party talks on funding social care and getting a solution that sticks for the long term.
"Neither the current players nor management were responsible for the club's relegation in 2012, so it was encouraging to hear the players and management reiterate their commitment to the remaining battle ahead of us all this season.
Both men began discussions by reiterating their commitment to fighting international terrorism.
They also reiterated their commitment to developing a coordinated response by early November.
Allied Irish executives reiterated their commitment today to Allfirst and the American market.
On opening night, several prominent artists reiterated their commitment to the theater.
These countries also reiterated their commitment, under the eThekwini Declaration, to allocate 0.5 percent of their G.D.P. to sanitation.
