The bank announced it would buy assets from all three of the funds in which dealings were suspended on Monday following the discovery of "potential irregularities in the valuation of unquoted securities".
Peter Young, the Deutsche Morgan Grenfell fund manager at the centre of investigations into suspected irregularities involving pounds 1.4bn worth of funds, remains suspended and has been replaced by Stuart Mitchell for the two funds he managed.
Separately, it emerged that one of the funds managed by Young, a 38-year- old high-flying fund manager, had apparently exceeded regulatory limits for the amount which could be invested in unquoted securities.
Under guidelines issued by the Securities and Investments Board, unit trusts may normally invest only 10 per cent of their funds in unlisted securities.
But up to 28 percent of one of his funds, Morgan Grenfell European Growth Trust, was invested in unquoted securities at the end of May, according to the unit trust's annual report.
Morgan Grenfell Asset Management, the fund management unit, said it would resume dealings tomorrow in the three suspended funds, in which 90,000 investors have stakes.
"The fund managers will meet their liabilities in respect of any irregularities identified in the course of the investigations into the three funds," a spokesman for Morgan Grenfell said last night.
"With a view to protecting investors' interests, Deutsche Bank has bought certain of the funds' securities for its own account, so that the prices at which the funds recommence dealing should not be affected by such irregularities," he added.
The irregularities centred on the valuation of unquoted, unlisted securities, often difficult to value because they do not have a price set on the stock market like listed securities.
Fund managers may be able to exceed their 10 per cent limit if they can prove to their trustees that the companies in which they are taking stakes are in the process of gaining stock market listings through privatisations or flotations. Sources close to Morgan Grenfell insisted last night that this was the case with the funds managed by Mr Young.
Mr Young, it has emerged, requested the "retirement", or resignation, of the Morgan Grenfell European Growth Trust's trustees, the insurer General Accident, in late June this year.
The usual reason for the retirement of a fund's trustee, which can happen at any time, is that the fund manager believes that trustee services can be obtained more cheaply or efficiently elsewhere. General Accident was replaced by Royal Bank of Scotland.
One City fund manager, who declined to be named, said: "It is hypothetically possible for someone to sack trustees in order to cover something up or because of other disputes with them. But this is unlikely because they would soon be found out."
Mr Young ran another of the funds in which dealings were suddenly halted at the start of the week - Dublin-listed Morgan Grenfell European Capital Growth Fund.
Another manager, Stewart Armer, who has not been suspended, ran the other troubled fund - Morgan Grenfell Europa.
Europa was the top performing fund last year, according to performance measurement firm Micropal, before crashing to 95th place by August.
Morgan Grenfell European Growth was second to Europa in 1995 but had fallen to 127th at the start of August.
Mr Mitchell, the fund manager replacing Mr Young, joined Morgan Grenfell nine years ago and managed third-ranking Morgan Grenfell European Profund from its launch in 1990 until February this year.
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