Saudi Arabia has denied holding talks with Israelis, including a meeting with Prime Minister Ehud Olmert.
Israelis say no talks have been held with King Abdullah
The official news agency quoted a foreign ministry official saying the story was "utterly false".
It would be the first official meeting between Saudi Arabia and Israel, which do not have diplomatic relations.
On Monday, Israeli reports quoted unnamed officials as saying that Mr Olmert had met King Abdullah or another senior Saudi royal on 13 September.
Later Israeli officials, including the prime minister, publicly denied any direct contact with the king himself, but not with lower level Saudis.
Saudi Arabia is the author of a plan which offers Israel diplomatic recognition from all Arab states in return for a complete withdrawal from the territory it occupied by Israel in 1967 and a negotiated solution to the 58-year Palestinian refugee issue.
Israeli media said Saudi and Israeli had discussed the Saudi peace initiative and Iran's nuclear programme.
Both countries are close regional allies of the United States.
Last week in an interview with Yediot Aharonot newspaper, Mr Olmert praised King Abdullah's "wisdom and sense of responsibility" and said he was very impressed by "public and other" statements and moves made by the kingdom.
Mr Olmert's Kadima party won Israeli elections in March with a pledge to withdraw unilaterally from parts of the occupied West Bank, while holding onto the settlement blocs where most Israeli settlers live.
The plan was shelved during the conflict this summer between Israel and Hezbollah militants in Lebanon.
Saudi Arabia was one of the countries calling for an immediate ceasefire in that conflict, but condemned Hezbollah's "reckless adventurism" for capturing two Israeli soldiers in a cross-border raid at the start of the conflict.