BEIRUT, Lebanon (AP) _ Assistant Secretary of State Richard Murphy made a lightning visit Friday to west Beirut to meet with Acting Prime Minister Salim Hoss.

Meanwhile, Syrian troops rounded up about 20 men after a Syrian soldier was shot and killed and another was wounded by unidentified gunmen, police said. The action followed a new wave of kidnappings and assassinations in the Moslem sector of the Lebanese capital.

After his 45-minute meeting, Murphy told reporters he was in Lebanon ''to have a discussion ... about the current situation in this country.''

The State Department banned the travel of Americans to Lebanon in January during a wave of kidnappings and militia fighting in the Moslem sector.

Murphy later crossed the Green Line, which divides the city's Christian and Moslem sectors, for a three-hour meeting with President Amin Gemayel, a Maronite Catholic. After the talks, he left aboard a U.S. Army helicopter for Cyprus.

He was accompanied by U.S. Ambassador John Kelly. They drove across the demarcation line in a bulletproof limousine.

Murphy said his talks were aimed at ''bringing the Lebanese factions together again. United for the better future of the country. As simple as that.''

He made no mention of 23 foreigners, including eight Americans, who are missing after being kidnapped in Lebanon. In addition, Anglican Church envoy Terry Waite is missing after he vanished last January during a mission to mediate with the pro-Iranian group Islamic Jihad, or Holy War, which holds some of the hostages.

On Thursday, Murphy was in Damascus where he held talks with Syrian Vice President Abdul-Halim Khaddam, architect of Syrian policy in Lebanon.

The visits came after news reports said the United States would try to mediate an end to a feud between Gemayel on the one hand and Syria and its Lebanese Moslem allies on the other.

Syria and Gemayel have been at odds since January 1986, when the Lebanese president vetoed a Damascus-backed peace accord among the country's main Christian and Moslem militias.

The Syrians, who have maintained 25,000 troops in north and east Lebanon, deployed an additional 7,500-man force in west Beirut last February to end militia anarchy in the 12-year civil war.

More than 100,000 have been killed in fighting, primarily between Druse, Shiite Moslem and Christian militias.

Police said unidentified gunmen in a car opened fire from Soviet-made AK-47 assault rifles at three Syrian soldiers in west Beirut's Sakiet al-Janzeer district Thursday night, killing a private and wounding another.

The Syrian crackdown Friday also followed the assassination of two leftist militia officials since Thursday and the kidnapping of three wealthy men, apparently for ransom, since Oct. 1, a police spokesman said.

The body of Tewfik Safadi, a member of the leftist Syrian Social Nationalist Party, was found early Friday, said the spokesman, who spoke on condition of anonymity.

Safadi, 36, was kidnapped Thursday from the offices of the party's magazine, a few hours after the assassination of Habib Keyrouz, 35, the spokesman of a rival wing of the divided party.

Police linked the killings to a power struggle within the party between pro-Syrian and pro-Palestinian factions.

The party advocates the merger of Syria, Lebanon, Jordan, Iraq, pre-1948 Palestine, Kuwait and Cyprus into one state, or Greater Syria.