BEIRUT, Lebanon--Israeli tanks and troops surged into west Beirut yesterday, and their gunboats opened up with missiles in a new offensive against Lebanese leftists and Palestinian guerillas following the assassination of President elect Bashir Gemayel

The gunboats opened fire on the oceanside neighborhood of Rouche and the Carlton Hotel area after a ground penetration of about 2.5 miles into west Beirut that the Tel Aviv command said was aimed at preventing a dangerous new linkup between the leftists and some 2000 PLO guerillas reported still in the city.

It was the first time the Israelis had gone into west Beirut in force since they invaded Lebanon 14 weeks ago to rout the PLO Several thousand guerillas are still in the country many of them in the eastern Bekaa Valley camped with some 25,000 Syrian troops whom the Israelis also want out

The Moslem half of Beirut was shaken by the naval bombardment as Gemayel's funeral was conducted in a solemn Maronite Christian rite at the packed church in his hometown of Biklaya, 12 miles east of Lebanon's capital

The death of Gemayel who was to become president next week, threatened to plunge Lebanon into a new round of warfare The presence of Israeli troops and Syrian forces in eastern Lebanon also carried the threat of a new confrontation between those two countries

Gemayel Mourning

Weeping bodyguards in the brown uniforms of Gemayel's Phalange Party threw themselves across his flag draped collin as the Mass was read in Arabic at Biklaya's St Abda's church

The wooden casket was then placed on an army gun carriage and taken in a slow moving procession to the cemetery A 21 gun salute echoed across the mountain peaks of central Lebanon as the 34 year old slam leader was lowered into his grave to the drumbeat of an army band