Binali Yildirim, a close ally of Turkish President Recep Tayyip Erdogan, took over the premiership in May from Ahmet Davutoglu who had spearheaded a policy of projecting Turkish power in the region.
Some analysts have suggested that Davutoglu made way for Yildirim to allow a more reconciliatory foreign policy that would allow Turkey to mend bridges with its enemies and return to its former dictum of "zero problems" with neighbours.
"Israel, Syria, Russia, Egypt... we cannot have permanent enmity with these countries which border the Black and Mediterranean Seas," Yildirim said in his first major interview with Turkish reporters, quoted by the Hurriyet daily.
'See big picture'
Relations with Russia tumbled to post Cold War lows when Turkey on November 24 shot down a Russian warplane over the Syrian border.
Moscow then blocked the sale of tours to Turkey, wrecking tourism in the south of the country where the industry was hugely dependent on Russian tourists.
"We need to look at the big picture," said Yildirim. "There is no hostility between our peoples. It's possible to go back to the old days and take our relations even further."
His comments come after President Recep Tayyip Erdogan sent a letter this month to his Russian counterpart Vladimir Putin congratulating him on Russia's national day, the first such high level contact since the plane crisis.
Russia has so far responded cooly, but pro-government daily Yeni Safak said Friday Turkey had prepared a nine step "roadmap" for normalising political and economic relations by September 1 and full ties by December 15.
Previously tight relations between key NATO member Turkey and Israel were downgraded over the 2010 deadly storming by Israeli commandos of a Turkish aid ship bound for Gaza, which left 10 Turkish activists dead.
Yildirim said Turkish diplomats were working on a solution for normalisation, with the lifting of the Israeli blockade on Gaza the key condition.
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"I don't think the remaining period will be very long" until a result for normalisation is achieved, he said.
Turkish press reports have suggested a breakthrough may come soon, with Ankara keen to wrap up the issue before the Turkish foreign ministry's powerful pointman on Israel, Feridun Sinirlioglu, takes up a new job in New York as Turkey's representative to the United Nations.
'Turkey wants Egypt ties'
Relations with Egypt suffered a similar downturn after the 2013 ousting of Egyptian president Mohammed Morsi, a close Ankara ally, and Erdogan has denounced President Abdel Fattah al-Sisi as an "illegitimate tyrant".
Yildirim said Ankara would never accept the 2013 "coup" but said "this should not be an obstacle in the commercial relations between our countries".
"The development of relations is in the interest of the two peoples," he added.
Reports have suggested that Turkey's increasingly close ally, fellow Sunni Muslim power Saudi Arabia, is keen to engineer a reconciliation between Cairo and Ankara.
On the Syria conflict, Turkey has always called for the ousting of President Bashar al-Assad and opposed attempts by Syrian Kurds to carve out an autonomous region.
"The territorial integrity of Syria is important for us," Yildirim said.
Foreign Minister Mevlut Cavusoglu Friday met US Deputy Secretary of State Antony Blinken in Ankara, telling him of Turkey's anxieties over the US support of Kurdish militias in Syria, foreign ministry sources said.
Turkey however has denied suggestions it may be prepared to soften its position that Assad must depart immediately for there to be a solution in Syria.
"Would you (as a refugee) be convinced to return to Syria if Assad is to stay and kill your family again? It's not feasible," a senior Turkish official said this week.