Synonym of SOLICIT

Beseech : ask (someone) urgently and fervently to do something; implore; entreat.
Demand : an insistent and peremptory request, made as of right.
Claim : state or assert that something is the case, typically without providing evidence or proof.
Require : need for a particular purpose.
Solicit : ask for or try to obtain (something) from someone.

Synonym of Solicit is Beseech