Malaysia is asking other Indian Ocean islands near French-owned Reunion to be on the lookout for more possible debris after a wing part suspected of being from missing flight MH370 came ashore.
The Malaysia Airlines plane, carrying 239 people, vanished in March 2014.
The Boeing-777 was travelling from Kuala Lumpur to Beijing.
The wing part discovered on Wednesday has been taken to mainland France for tests. But other items found at the weekend were not from an aircraft.
The BBC's Karen Allen, on Reunion, says one of the pieces was found on a rocky beach just north of where the suspected plane wing part was spotted.
A team of police and police photographers was called and the object was taken away.
However, Malaysia's Director General of Civil Aviation Azharuddin Abdul Rahman told Associated Press: "I read all over media [the new debris] was part of a door. But I checked with the Civil Aviation Authority, and people on the ground in Reunion, and it was just a domestic ladder."
The Agence France-Presse news agency said on Sunday that one of its photographers had also seen a mangled piece of metal inscribed with two Chinese characters, attached to a leather-covered handle and measuring 100 sq cm being placed into an iron case and carried away.
But some social media commentators suggested it might be a kettle.
A source close to the inquiry told AFP that "no object or debris likely to come from a plane" had been submitted as evidence on Sunday.
A spokesman in the town of St Andre, where the wing part was found, said that while people were more vigilant, "they are going to think any metallic object they find on the beach is from flight MH370".
"But there are objects all along the coast, the ocean continually throws them up," Jean-Yves Sambiman told AFP.
Malaysia's transport ministry says it now wants to expand the search for more debris around Reunion.
Malaysia will ask regions nearby to alert it if they find any debris that could be from MH370.
Transport Minister Liow Tiong Lai urged the regions to allow experts "to conduct more substantive analysis should there be more debris coming on to land".
But he also urged people to allow the inquiry to run its course "for the sake of the next of kin of the loved ones of MH370 who would be anxiously awaiting news and who have suffered much over this time".
An Australian-led search effort for the plane has so far focused on a vast area of the southern Indian Ocean about 4,000km (2,500 miles) to the east of Reunion.
No physical trace of the aircraft had been found.
Mr Liow earlier confirmed that the object found on a beach at St Andre on Wednesday was a wing flap from a Boeing 777 - the same type of aircraft as the one that vanished.
The piece has gone to mainland France, where investigators in the city of Toulouse will seek to establish if it came from MH370. They will begin their work this Wednesday.
Fragments of a suitcase found on the same beach are also to be examined.
Investigators believe MH370 veered off course on the way to Beijing and crashed into the sea - but they do not know why.