David Cameron has said Britain will never "retreat from the world" and it is in Europe's interests for the UK to stay in a reformed European Union.
Speaking in Hamburg, the PM said changes he was seeking to UK membership would make Europe "more outward-looking, competitive and dynamic".
He said if he got what he wanted he would campaign "unequivocally" for the UK to stay in.
Campaigners for EU exit have said the PM's renegotiation is a sham.
The prime minister is hoping for a deal at next week's summit of EU leaders in Brussels to allow him to put the new terms of membership to the British public in a referendum in June.
But Donald Tusk, the European Council president who is brokering talks on the UK's renegotiation process, has warned that the political process remains "very fragile", with some leaders still harbouring reservations about the plan, particularly over limits on welfare payments to new EU migrants.
In his final major speech before next week's crunch meeting, Mr Cameron told business, political and civic leaders in Hamburg that he made no apology for Britain being "argumentative and rather strong-minded" when it came to the subject of Europe.
"We have the character of an island nation - independent, forthright, passionate in defence of our sovereignty - and of institutions that have served us well for many hundreds of years," he said.
"And the need to protect our sovereignty has always been paramount for us."
But he told his audience at the Matthiae-Mahlzeit dinner - which included German Chancellor Angela Merkel - that Britain was an "open nation" and the values it shared with Germany underpinned their co-operation on trade, enterprise and security.
Downing Street said the prime minister and Mrs Merkel also held a meeting - agreeing that EU countries and institutions needed to continue to work together to reach a deal on the UK's renegotiation.
Other topics discussed included migration and implementing the £6.8bn in pledges made by countries at last week's London conference to help Syrians affected by the five-year conflict, a Number 10 spokesman said.
By BBC Political Correspondent Iain Watson
David Cameron has been denounced by some of his own MPs for negotiating a "threadbare" deal, and more than 100 of his councillors are urging him to campaign to leave the EU.
The tone of his speech in Hamburg suggests he will do no such thing - he pledged to campaign "unequivocally" for British membership on new terms, though included in his speech was his usual disclaimer that he "rules nothing out" until a deal is done.
We also got another glimpse of how the referendum will be fought - with a strong plea for Europe to "stand together" in an uncertain world.
But there was a recognition that he won't get everything he wants, when he said: "Even when we have secured the changes I am arguing for, the job will not be done."
He portrayed Germany as an ally in arguing for further change but his opponents will pounce on this as evidence of the paucity of his demands.
In his speech, Mr Cameron argued it was in the two countries' interests for the EU to become more competitive and for rules to ensure that both countries inside the eurozone and those outside could be mutually successful.
"When Britain says we need to have a Europe that respects nation states and that we should be able to run our own welfare systems, those are calls which I believe resonate around Europe," he said.
"So if by working together we can achieve these changes, then I will unequivocally recommend that Britain stays in a reformed European Union on these new terms. Of course, if we can't then I rule nothing out.
"But I believe we can - and if we do, I believe we can win that referendum and that will be good for Britain, good for Germany and good for the whole of Europe."
Negotiations on the final wording of the deal - which includes an "emergency brake" on benefit payments to EU migrants and a UK opt-out from "ever closer union" - look set to carry on right up to the start of the summit on 18 February.
A senior Tory backbencher has said that up to 100 Conservative MPs could end up supporting the Out campaign in a future referendum, including a number of current Cabinet ministers.
More than 130 Conservative councillors have warned the prime minister risks splitting the party unless he accepts his renegotiation has failed and he campaigns for Britain to leave the EU.
Further reading on the UK's EU referendum
EU renegotiation: Did Cameron get what he wanted?
Referendum timeline: What will happen when?
The view from Europe: What's in it for the others?