* China's vice-premier offers better ties with EU
* EU warns Chinese telecoms row is unresolved
* EU, China to sign investment deal next month
By Robin Emmott
BRUSSELS, Oct 24 (Reuters) - China and the European Union sought to mend ties on Thursday after narrowly avoiding a trade war this year, but the EU's trade chief told Beijing to stop handing out state subsidies that Brussels says are illegal.
Europe is China's most important trading partner and for the EU, China is second only to the United States, but the bilateral relationship has been bedevilled by a series of damaging trade rows ranging from steel and wine to solar panels.
"China is ready to work with the European Union to set out a comprehensive plan for the future of EU-China relations," China's Vice-Premier Ma Kai told a news conference alongside the EU's two most senior economics and trade officials.
"China is ready to ensure that our cooperation can be elevated to a higher level," Ma said after talks with the EU's economics chief Olli Rehn and EU Trade Commissioner Karel De Gucht in Brussels.
Saying he had come to send a "clear and positive signal" Ma, a one-time state planner promoted in China's new government this year, welcomed the start of negotiations with the European Union on Nov. 21 at a summit in Beijing that will seek to remove restrictions on EU investment in China.
The European Union wants greater access to China in industries including banking and is eager for Beijing to drop requirements that Europeans must work with a Chinese joint venture partner and hand over sensitive know-how.
EU officials say the so-called investment pact is a fundamental test of China's willingness to compromise and play by rules set down by the World Trade Organisation that ban subsidising of companies to undercut foreign competitors.
A successful EU-China investment agreement could pave the way for a wider free-trade accord in the future. But for now, there is friction as China seeks to produce the kind of sophisticated products that compete directly with Europe.
Despite doubling trade with China since 2003, the European Union accuses Chinese companies of benefiting from unfair state aid allowing them to dump goods in Europe, selling them at below cost to put locals out of business.
"The whole system of subsidies is one of the major problems in our trade relationship," said De Gucht, referring in particular to Chinese export credits.
He warned that the European Commission remained ready to launch an investigation into anti-competitive behaviour by Chinese producers of mobile telecommunications equipment, the next potential flashpoint in bilateral trade ties.
"This problem has not gone away," he said.
The Commission told Beijing in May it was ready to open an anti-dumping and anti-subsidy investigation into Huawei, the world's number two telecoms equipment manufacturer, and ZTE , the world's fifth largest producer.
However, De Gucht is first seeking a negotiated solution.
China exports network equipment, base stations and connections used by telecoms providers worth more than 1 billion euros ($1.4 billion) a year to the European Union, giving it almost a quarter of the EU market.
De Gucht said he did not talk about specific cases with Ma but held an extensive telephone conversation with Chinese Minister of Commerce Gao Hucheng this week.
In the interests of EU-China trade, De Gucht is eager to avoid launching a telecoms investigation because of the sharp tensions caused by the last major dispute over solar panels - by far the biggest between China and the EU.
European companies accused Chinese rivals of dumping about 21 billion euros worth of solar panels at below cost in Europe last year, putting European firms out of business.
Brussels initially moved to impose punitive duties on Chinese solar panels but Beijing threatened sanctions on goods including German cars and French wine. Both sides agreed a minimum price for panels from China in July.
In a goodwill gesture, the EU hopes China will halt its anti-dumping inquiry into European wine sales, but De Gucht and Ma declined to comment on this on Thursday.