Shares in oil major BP rose 2.7 percent on Tuesday, taking their bounce this month to 28 percent, on signs the Gulf of Mexico oil spill could be contained and on hopes of asset disposals.

BP shares traded at 409.8 pence on Tuesday after hitting a near 14-year low of 296 pence on June 25 on concerns over the cost of the oil spill, the worst in U.S. history.

However, technical analysts said BP shares face major resistance around 435 pence -- the 38.2 percent Fibonacci retracement level of the stock's slump from mid-April to the low hit in June -- and said investors should consider taking profit as the stock approached that level.

There is potentially major overhead resistance to contend with between 430 -- a level we consolidated above before plunging in early June and then slightly higher again at 434.50 -- the 38.2 percent Fibonacci retracement target, said Geoff Wilkinson, head of investment research at Mint Securities in London.

Both have the implicit technical potential to attract profit-taking.

The stock faced the next major resistance at 477 pence, the 50 percent Fibonacci retracement level.

BP said on Tuesday talks on the divestments were making progress, though it declined to identify the potential buyers or the assets up for sale.

Despite the bounce, BP shares were still down nearly 38 percent since the oil leak started in April.

You have got the fact that this stock, if left alone, could potentially recover. It's talking about selling assets. It's pulling a huge defense together to fend off any potential takeover targets, said Yusuf Heusen, sales trader at IG Index in London.

Ultimately, it's going to be sensitive as to what happens with the relief well, we don't know whether this containment cap has actually worked yet. There is still endemic risk in the stock, but far less than before. (Reporting by Dominic Lau, Blaise Robinson and Atul Prakash; Editing by Hans Peters)

Oil Spill