* Greek shares rise further, adding to gains on Monday
* Equities also boosted by pick-up in euro zone PMI data
* Numericable slips as French govt opposes Bouygues deal
* Europe bourses in 2015: link.reuters.com/pap87v
* Asset performance in 2015: link.reuters.com/gap87v
By Sudip Kar-Gupta
LONDON, June 23 (Reuters) - European shares climbed to a three-week high on Tuesday, extending the previous session's rally on expectations that Greece was getting closer to a debt deal.
Greece's ATG share index rose 5.3 percent, adding to a 9 percent surge in the previous session, while the country's benchmark banking index advanced 8.8 percent.
The Athens' ATG index remains down around 5 percent since the start of 2015, due to Greece's debt problems, but it has recovered from a slump last week.
The euro edged back, with some currency traders citing a range of still-formidable political barriers to a Greek debt agreement as weighing on the currency.
However, many other investors were confident of a deal.
Greece presented new budget proposals that euro zone leaders welcomed as a basis for a possible agreement to unlock frozen aid and avert a looming default.
"It now appears that we will have a short-term solution to the problems," said Andreas Clenow, hedge fund trader and principal at ACIES Asset Management.
The pan-European FTSEurofirst 300 index rose 1.5 percent to its highest level in three weeks.
The euro zone's blue-chip Euro STOXX 50 index - which had risen 4.1 percent on Monday in its biggest one-day percentage gain since August 2012 - also climbed 1.4 percent.
Clenow expected a compromise to the Greek debt situation to push European markets back up to peak levels reached earlier in March and April, with the FTSEurofirst still up around 16 percent since the start of 2015.
Numericable-SFR edged back 1.4 percent after France's economy minister said a bid by Altice - which is Numericable's majority owner - for Bouygues Telecom risked creating an operator that was "too big to fail" and could threaten jobs.
However, Paris' broader CAC equity index rose 1.5 percent to go back within sight of its highest level in more than seven years, as a resurgence of activity in France helped euro zone businesses expand at their fastest rate in four years this month.
"The European economy has enough positives to herald a strong recovery even without an ever-falling exchange rate," said Tim Crockford at Hermes Investment Management.
Today's European research round-up (Additional reporting by Atul Prakash; Editing by Alison Williams)