By Rae Wee

SINGAPORE (Reuters) - The euro hit a two-week low on Tuesday as a worsening downturn in euro zone business muddied the bloc's rate outlook against a still-hawkish European Central Bank (ECB), while the dollar rose ahead of this week's trio of major central bank meetings.

The offshore yuan strengthened in early Asia trade, following comments from China's top leaders on Monday pledging to step up policy support for its flailing economy.

The euro was shaky at $1.1063, up just 0.02% having slumped to a two-week low of $1.1059 earlier in the session, after a survey on Monday showed euro zone business activity shrank much more than expected in July, reigniting recession fears.

The single currency had slid more than 0.5% in the previous session.

"The extension of the weakness in the manufacturing sector as well as services, and Germany, in particular, being a lot weaker than expected ... that's putting some question marks around the rhetoric that we should expect from the ECB on Thursday," said Rodrigo Catril, senior currency strategist at National Australia Bank (OTC:NABZY) (NAB).

Markets have fully priced in a 25-basis-point rate hike by the ECB at its meeting this week, though the path of future rate increases beyond July remains up in the air.

Elsewhere, sterling fell 0.11% to $1.2811, while the U.S. dollar index steadied at 101.39.

Flash PMI survey similarly out in the UK on Monday showed Britain's private sector growing at its weakest pace in six months in July, while a separate survey pointed to U.S. business activity slowing to a five-month low this month.

The Federal Reserve also meets this week and is expected to deliver a 25 bp rate hike, with a majority of economists polled by Reuters expecting that to mark the last increase of the central bank's current tightening cycle.

"While the Fed meeting (in July) is likely to be uncontroversial in terms of the decision on interest rates, the Fed's statement and the press conference will be extremely relevant for markets," said Guillermo Felices, global investment strategist at PGIM Fixed Income.

"Incoming activity data has been stronger than expected in June and July," he said. "The Fed will have to explain what they make of the resilient U.S. economy."

The yen remained under pressure at 141.43 per dollar, struggling to recover from its heavy losses on Friday on a Reuters report that the Bank of Japan is leaning towards keeping its yield control policy unchanged at this week's policy meeting.

The offshore yuan rose nearly 0.5% to 7.1540 per dollar, with investors encouraged by comments from China's top leaders at the closely-watched Politburo meeting signalling more support for its weakening economy, though many were still seeking out specific details on greater stimulus measures.

"We view the assessment of the economic growth situation and description around the property market as slightly more dovish than expected, though we still await specific easing measures after (the) statement," said analysts at Goldman Sachs (NYSE:GS) in a note.

"We continue to expect a combination of monetary, fiscal, property and consumption support measures to be rolled out in the next few months."

The Australian dollar, often used as a liquid proxy for the yuan, gained 0.18% to $0.67515, while the kiwi rose 0.06% to $0.6209.