Two ancient artifacts illegally removed from Greece decades ago went on display in Athens on Wednesday after a US-based collector was persuaded to repatriate them, the Greek culture ministry said.

The upper part of a marble funerary stele and a bronze krater, or large cup, dated to the 5th and 4th century BCE, were returned by collector Shelby White in August under a deal in which Greece pledged not to legally pursue the matter, it said.

"The culture ministry recognises that the antiquities were acquired by Ms White in good faith, and for this reason...no demands will be raised against (her)," a ministry statement said.

But Greece reserves its legal rights over other potential claims regarding items in White's collection, it added.

White and her late husband, New York financier and philanthropist Leon Levy, accumulated one of the finest US collections of Roman and Greek antiquities.

The funerary stele depicting a youth and a warrior was found in the early 1960s in Porto Rafti, a coastal resort east of Athens.

Three decades later, a Greek archaeologist identified its missing upper fragment in the White-Levy collection from a New York Metropolitan Museum exhibit catalogue. The Greek state filed a claim for the item last year.

The two fragments will now be reunited at the local Museum of Vravrona for the first time in decades, the ministry said.

The bronze krater, a vessel in which the ancient Greeks mixed wine and water, was likely looted from a royal tomb in the northern region of Pieria, Greek archaeologists believe.

Both items will be temporarily displayed at the National Archaeological Museum in Athens.

A country rich in antiquities targeted by looters for nearly 200 years, Greece has lately stepped up efforts to reclaim items illegally exported abroad, many of which are in private collections or major museums.

"The pillage of antiquities has been particularly traumatic for small countries with rich history such as ours," Greek Culture Minister Michalis Liapis said on Wednesday.

"Hence their repatriation is of great importance to the Greek people."