The part of the sentence "urges that he" is correct and can definitely be used in written English.
You could use it in situations where someone is recommending or strongly suggesting that someone else should do something. For example: "My father urges that he take more time to himself and relax."
Practically everyone Nossiter meets urges that he visit the Hotel du Portugal, where a small Gestapo contingent tortured local members of the Resistance.
A man as steeped in the puritan, idealistic mores of his era as Baden-Powell clearly was might well have been too repressed to act on urges that he, and everyone in his social circle, would have considered not only transgressive but sinful.
The President pro tempore of the Senate has survived (with minor injuries) and, on learning of the Speaker's condition, urges that he be sworn in as Acting President for the sake of providing leadership to a stricken nation - just as soon as they can find the Chief Justice of the Supreme Court to provide a favorable interpretation of the law.
In their session, he says he needs to curb the urges that he's been having ever since he was little.
He urges that science be taught so as to take "its rightful place alongside music, art, and literature".
But he never responded to Kepler's urging that he stand forth in his opinions.
Born into a wealthy family, Barnet rejected their urging that he become a corporate lawyer and instead turned to music.
His supporters have urged that he be charged in the UK.
He rebuffed Democrats like Senator Robert Menendez who urged that he overhaul his campaign team, people briefed on the conversations said.
Federal prosecutors have urged that he be held as both a flight risk and a danger to the community.
A number of such groups sent a letter to President Clinton on Tuesday urging that he block approval.
