By Sujata Rao

LONDON, April 7 (Reuters) - Russian stocks tumbled more than 1 percent on Monday and the rouble slipped on worries over renewed tensions with Ukraine while broader emerging equities and currencies also eased, tracking moves on global markets.

Pro-Russian protesters seized official buildings in several eastern Ukrainian cities on the weekend, including the mining city of Donetsk. They demanded a referendum on whether to join Russia like that held in Crimea that paved the way for its annexation by Russia.

The fear of more confrontations between Russia and Ukraine hit Russian assets, with stocks fell to one-week lows after three straight weeks of gains. Blue chip shares such as Sberbank, Gazprom and Lukoil slipped 1-2 percent.

"The events show that the risk of further secessions is a very real one in coming months," UBS strategist Manik Narain said.

The rouble fell 0.6 percent to the dollar, and Russian 5-year credit default swaps rose 9 basis points to 219 bps.

Ukrainian assets also were punished, with dollar bonds losing around 1.0-1.5 points and CDS rising 14 bps.

Broader emerging equities slipped after three weeks of gains , tracking losses in developed markets which saw a pullback from record highs after March U.S. jobs data.

The data eased concerns about an early U.S. interest rate hike but also suggested the economy was still in recovery mode, a scenario generally seen as positive for emerging markets.

Narain said investors were hopeful of additional stimulus from China as well as the European Central Bank and as yields in peripheral Europe fell to multi-year lows, many fund managers could turn to emerging debt instead.

The past week has seen bond roadshows by higher-risk countries such as Pakistan, Zambia and Ecuador while Sri Lanka, rated BB minus, is also gearing up to sell debt.

"It all seems to reflect optimism on the stability of U.S. and eurozone rates. The back end of the Treasury curve has been very stable with low volatility and that's what EM issuers need," Narain said.

Zambia has opened books on a new 10-year dollar bond, with initial price talk at 8.75-8.875 percent, Thomson Reuters market service IFR reported on Monday.

In Hungary, financial markets slipped after the ruling Fidesz party's landslide win and big gains for the far-right opposition in elections. That sets the stage for four more years in power for Prime Minister Viktor Orban, whose policies are broadly seen as market-unfriendly.

Five-year Hungarian CDS rose 8 basis points on the day, but shares and the currency pared sharp opening losses . Shares in Hungary's biggest bank, OTP, fell almost 1 percent before recovering most of the losses.

"We expect a continuation of a strong anti-foreign capital, statist agenda, as well as a rhetorical and governing style designed to collide with the international community and the European Union," analysts at Eurasia said in a note.

The Turkish lira slipped 0.2 percent off three-month highs versus the dollar after the central bank governor signalled a possible cut to the 12 percent overnight lending rate. He stressed however the bank would decide the timing of any policy changes, reacting to Prime Minister Tayyip Erdogan's calls for an emergency rate cut.

Elsewhere, Nigerian assets were flat after the country rebased its economic data for the first time since 1990, almost doubling its gross domestic product figures and making it the biggest economy in Africa. Its public debt ratio stands now at just 11 percent of GDP.

"Investors will not be able to ignore the biggest economy in Africa and one that's ranked 26th in the world," said Razia Khan, an economist at Standard Chartered in London.

"But in the short-term I don't see any fall in borrowing costs...Investors will wait for (Feb. 2015) elections with the semi policy freeze and uncertainty associated with that."

For GRAPHIC on emerging market FX performance 2014, see http://link.reuters.com/jus35t

For GRAPHIC on MSCI emerging index performance 2014, see http://link.reuters.com/weh36s

For GRAPHIC on MSCI emerging Europe performance 2014, see http://link.reuters.com/jun28s

For GRAPHIC on MSCI frontier index performance 2014, see http://link.reuters.com/zyh97s

For CENTRAL EUROPE market report, see

For TURKISH market report, see

For RUSSIAN market report, see (Editing by Hugh Lawson)