* Sanctions over Ukraine targeted individuals not sectors
* Market had priced in more severe sanctions - analyst
* Share index gains knocked back after further unrest (Adds details and quotes, updates prices)
By Jason Bush and Zlata Garasyuta
MOSCOW, April 29 (Reuters) - Russian asset prices rose on Tuesday, reflecting investors' relief that new Western sanctions against Russia over Ukraine were less severe than many had feared, but shares gave up some gains after further civil unrest in eastern Ukraine.
At the close the rouble-denominated MICEX share index was up 0.4 percent to 1,305 points, while the dollar-denominated RTS had risen 1.2 percent to 1,153 points.
On Monday, when the new sanctions were announced, the MICEX rose 1.6 percent and the RTS 2.2 percent, having fallen 5.6 percent and 6.7 percent respectively the previous week.
"The new sanctions have caused a sigh of relief," Golden Hills Capital analyst Natalia Samoilova said in a morning note.
"The market had priced in far more serious sanctions against whole sectors of the economy."
The United States spared major listed companies or whole sectors, instead targeting individuals close to President Vladimir Putin and companies belonging to them, none of which are traded on the stock exchange.
Russian indexes had been up 1.2-1.8 percent shortly after opening, but later shed part of the gains, knocked by the seizure of another government building by pro-Russian protesters in the eastern Ukrainian city of Luhansk.
"Today the market reacted to the events in Luhansk. The fall in prices was small but all the same it was there," said Yury Khilov, head of trading operations at Deutsche Bank in Russia.
"As with previous days this month: in the absence of news, on thin volumes, the market rises, and with the appearance of alarming reports the volumes immediately increase."
Analysts said the question remained how the dispute will be resolved.
"The fall in the market last week was extremely serious: investors were preparing for the worst-case development of events, therefore they are now attempting to return to purchases," Investcafe analyst Mikhail Kuzmin said in a note.
"If the Ukrainian authorities return to active military operations and there are new victims, this could again destabilise the conflict situation."
Russia has said that it has the right to intervene militarily in Ukraine to protect Russian speakers, while the West has warned of much tougher sanctions if Russia invades.
"Of course we are only seeing short money. People are buying for a couple of weeks, no longer," said Alexei Evsyutin, responsible for retail sales at BCS brokerage.
Shares in leading oil company Rosneft, which had fallen 1.4 percent on Monday after its CEO Igor Sechin was sanctioned by the United States, rebounded by 1.7 percent on Tuesday. It was helped by a board recommendation late on Monday to boost its dividend pay-out by 60 percent.
The bond markets shrugged off a downgrade of six major state-owned companies by Standard & Poor's announced late on Monday, following its downgrade of the sovereign on Friday, instead reacting positively to the improved sentiment over sanctions.
The yield on Gazprom 2019 bonds fell to 5.74 percent, down from 6.01 on Monday. The yield on Russian Railways' 2017 bonds fell to 4.57 percent from 5.09 percent the previous day.
The rouble was also stronger on Tuesday, hitting a 10-day peak. At 1600 GMT it was 0.6 percent stronger at 35.62 against the dollar and by 0.8 percent to 49.21 against the euro, strengthening by 0.7 percent to 42.74 against the dollar-euro basket.
The rouble was also helped by German inflation figures, which were lower than forecast, making monetary stimulus by the European Central Bank more likely and weakening the euro.
Traders said that given the decline in Russian country risk, market players were reluctant to extend their foreign currency long positions over the Russian May holidays, leading to sales of forex in the days leading up to May 1.
"Paying 4 kopecks to extend the longs is reckoned to be too much," said a dealer at a large Western bank. (Additional reporting by Vladimir Abramov; Editing by Alison Williams)