Mr Abbas, a moderate who has pledged to use negotiation to rein in Palestinian militants, won last Sunday’s election.
His inauguration comes a day after Israel broke off contacts in the wake of a militant attack on a Gaza Strip crossing that killed six Israelis.
Israeli officials say Mr Abbas must act swiftly to halt militant attacks.
After his election, Mr Sharon called Mr Abbas to congratulate him and said he hoped to meet the new leader “soon”.
But by Friday hopes for a speedy meeting appeared to be dashed.
“Israel informed international leaders today that there will be no meetings with Abbas until he makes a real effort to stop the terror,” Mr Sharon’s spokesman Assaf Shariv said.