Israeli minister invites Lebanon's Aoun to direct border talks
Last week, Steinitz on Twitter accused Lebanon of undermining the talks by continuously shifting its position and trying to widen the disputed area under negotiation.
That sparked a Twitter response from Aoun, who rejected Steinitz's charges that Lebanon had been inconsistent.
Steinitz, in a series of tweets directed at Aoun on Monday, in both Hebrew and Arabic, said he had been "enjoying the dialogue that has developed between us in recent days".
"I am convinced that if we could meet face-to-face in a European country in order to have open, or secret, negotiations, we would have a good chance of resolving the maritime border dispute once and for all."
There was no indication on whether Aoun intended to respond to or accept the offer.
Israel and Lebanon have been negotiating based on a map registered with the United Nations in 2011, which shows an 860-square-kilometre (330-square-mile) sea area as being disputed.
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But Lebanon considers that map to have been based on wrong estimates.
According to Lebanese energy expert Laury Haytayan, Aoun's tweet confirms that it is now demanding an additional 1,430 square kilometres (552 square miles) of sea further south.
Agencies contributed to this report.