It was Semneby's second attempt in just over a week to persuade the two sides to modify their stance in order to reach some kind of consensus and end the three-week standoff in Tbilisi.
Semneby told journalists after his meeting with the opposition leaders that "it is important for this country, and it is also important for the European Union as a friend and partner of Georgia, that this situation that we have here in the streets is transformed into a political process."
He described as "interesting" the amendments to the election law and the system of government that the authorities have proposed as an alternative to Saakashvili's resignation.
Semneby also argued against either side setting preconditions for embarking on a dialogue: "One should not exaggerate steps that should be taken as preconditions. One should avoid talking about preconditions for negotiations to start. If one does that and adds one issue on top of the other, then we will never get the negotiation going."
Speaking late on May 1 on the TV channel Rustavi-2, Irakli Alasania, who heads the opposition Alliance for Georgia, agreed that the opposition should embark on talks with no preconditions while continuing its ongoing street rallies.
Opposition leaders have filed a formal request with the Tbilisi authorities to continue those protests until May 15 and Conservative Party leader Kakha Kukava was quoted on May 2 as saying that the tactics of picketing public buildings have proven effective and will not be modified.
Kukava rejected the term "stalemate," saying that "it is the authorities that are in a stalemate, not the opposition."
Alasania said on May 1 that within the next few days he will draft concrete proposals for overcoming the ongoing political standoff. He said he is certain that if talks with the authorities do indeed take place, it will prove possible to "find ways out of this crisis."
At the same time, he deplored the authorities' imputed failure to advance any "concrete proposals," and dismissed as "an ultimatum" Bakradze's statement earlier on May 1 that the opposition should make up its mind within days whether or not it wished to participate in the reform process Bakradze announced on April 26.
Former Foreign Minister Salome Zurabishvili, who heads the Georgia's Path opposition party, told journalists on May 1 that the opposition would agree to discuss Bakradze's proposals only if and when Saakashvili steps down.