The UN team's request on Tuesday came a week after Lebanese authorities arrested and later accused four pro-Syrian generals over the assassination.
In particular, the investigators wanted "any pieces of evidence such as vehicle parts, plastic, metal pieces or any other item related to the [Beirut] crime scene".
The request coincided with the Slovak secret service saying it was investigating reports that Syria bought some of the explosives used in al-Hariri's assassination from a Slovak-based company.
Opponents of Syria's role in Lebanon accuse Damascus and its Lebanese security service allies of involvement in al-Hariri's killing. Both authorities deny any role.
A Lebanese magistrate recently ordered the four generals be held in police custody until a trial begins to hear official charges against them.
They are former General Security chief Major General Jamil Sayyed; Major General Ali Hajj, the ex-Internal Security Forces director general; Brigadier General Raymond Azar, the former military intelligence chief; and current Presidential Guards commander Brigadier General Mustafa Hamdan.
A fifth Lebanese suspect identified by the UN team, former pro-Syrian lawmaker Nasser Qandil, was also questioned but released.
Since the UN probe began on 16 June, British and Lebanese divers have retrieved what apparently were several vehicle parts and metal pieces from the sea floor near the Beirut waterfront site where al-Hariri's motorcade was attacked.
Investigators want to find the remains of an explosives-packed Mitsubishi pickup truck that chief UN investigator Detlev Mehlis believes may have been used to kill al-Hariri, according to local media reports.
The UN says anyone aiding the request for more evidence won't be prosecuted and can remain anonymous.
Al-Hariri was killed in a blast in
Beirut in February
Last week, Mehlis said he felt more people beyond the four generals were involved in al-Hariri's assassination and had not yet identified any Syrian suspects but added there had been "problems" with Syrian cooperation.
Mehlis is expected to visit Syria on Saturday after Damascus, under intense pressure to cooperate with his probe, invited him to come.
He is expected to report to the Security Council before his three-month mandate expires on 17 September and seek an extension to the probe.
Meanwhile, Slovak authorities are looking into a report by a Paris-based internet publication, Intelligence Online, alleging that a Syrian military intelligence defector had told Saudi and US intelligence agencies that 1000 kilograms of RDX explosive used in the al-Hariri attack were bought from a Slovak company.
"We have this information ... and it is at the stage of being investigated," said Vladimir Simko, a Slovak Information Service spokesman.
The report said: "The Syrians bought a large quantity of the explosive through the intermediary of a Syrian businessman close to military intelligence who has an office in Istanbul." There was no immediate Syrian comment.