* Economy shrinks 3.4 pct year on year in Q3; faster than Q2
* Jobless rate rises to 15.8 pct from 15 pct in Q2
* Prime Minister urges patience with austerity measures
* Grim data coincides with national strike
By Axel Bugge
LISBON, Nov 14 (Reuters) - Portugal's economy slumped further and unemployment hit a record in the third quarter, highlighting concerns the country is entering a recessive spiral as it readies for its biggest tax hikes in decades.
Gross domestic product shrank for the seventh quarter running, dropping 3.4 percent year on year compared with previous quarter's revised 3.2 percent fall, National Statistics Institute INE said on Wednesday.
It said growth in exports - the only positive factor for the economy during its crisis - had slowed. Domestic demand remained weak, hit by the spending cuts and tax increases imposed under an international bailout whose terms the government is struggling to meet.
The jobless rate rose to 15.8 percent from 15 percent in the second quarter and 12.4 percent a year earlier.
"The trajectory (of unemployment) remains clear and without any signs of changing, with the economy incapable of generating jobs," said Filipe Garcia, head of Informacao de Mercados Financeiros, a consultancy.
The continuation of what is the country's deepest recession since the 1970s tracked extended economic slumps elsewhere on the euro zone's ailing periphery.
Data from Athens showed Greece's gross domestic product shrank 7.2 percent year-on-year in the third quarter, also faster than in the previous quarter.
Unions in Portugal and in Spain - where the economy also stayed in recession in the third quarter and unemployment stands above 25 percent - staged general strikes on Wednesday.
Prime Minister Pedro Passos Coelho, whose government will enforce Portugal's biggest tax increases in modern times next year, urged patience with the austerity drive on Wednesday.
"We are fulfilling a very tough adjustment process, not in order to show our obedience, but because this way we make our country recover," he said in televised remarks. "We have to lower our level of spending in line with our possibilities."
Passos Coelho, who won backing for the belt-tightening from German Chancellor Angela Merkel during a visit to Lisbon on Monday, also said the government was sticking to this year's budget deficit goal of 5 percent of GDP.
Youth unemployment, a key indicator of Portugal's poor job prospects, rose to 39 percent from 35.5 percent, INE said.
In what was its preliminary estimate of GDP, INE said that, quarter on quarter, Portugal's economy shrank 0.8 percent compared with 1.1 percent in the previous three months.
The institute said exports rose less than previously.
"By quarterly comparison, the drop was sharper than we expected probably due to an export slowdown related to stevedores strikes and weaker exports to Spain, our main partner," said Teresa Gil Pinheiro, economist at Banco BPI in Lisbon.
INE said domestic demand had a less negative impact than previously on a yearly basis.
But many economists expect demand at home to slump through the end of the year and into 2013.
"We don't know the breakdown of GDP, but the decline in private consumption is weighing on it," said Rui Barbara, an economist at Banco Carregosa. "People must be already anticipating the austerity to come next year."
The centre-right government expects the economy to contract 3 percent this year and 1 percent in 2013. The country's central bank expects a sharper drop of 1.6 percent next year.